Here's another fun thing: rewatching the earlier episodes (all 5 seasons) with an eye towards moments that take on a different light when you realize Bashir is genetically enhanced and covering it up (even though the writers and actors didn't know this at the time). I find it works remarkably well. This post will list some of these moments. And there's a lot.
First, in general you can say that Bashir was hiding some of his more advanced abilities (like racketball, tennis, dart throwing, rapid mental calculations) all of his life, of at least since he found out at age 15. But I think that he probably never really held back when working on medical problems. He would never have been OK with people dying just so that he could keep his genetic enhancements secret. I think that his memory skills and hand-eye-coordination, etc, all those skills that made him a great doctor, had been enhanced to a great level certainly, but not to a level beyond possibility for a non-enhanced person. Laypeople understand so little about medicine anyway. Most laypeople see doctors as already amazing and magical. No matter what outrageous things he does (like bringing people back from the dead; mentioned early on in "The Passenger") most people will just think he's just like all other doctors. It's only when he does things to get the attention of other doctors (like graduating at the top of his class would have; or like being the youngest person to be nominated for the Carrington Award in "Prophet Motive") that he needs to worry too much about what he does in medicine. It's the enhanced non-medicine things that he does that cause him more problems.
Remember the short scene at the beginning of "A Man Alone" where Bashir tries his hand at the Altonian brain teaser that Dax had been trying to master for over 140 years? Bashir tries the game (with Dax present) and does horribly. She jokes that he must have "something on his mind" and then leaves, but encourages him to try the game again. As the scene ends we hear Bashir say "computer, reset" but we don't see his next attempt at the game. I think that with Bashir's genetically enhanced and structured mind that this game would actually not be all that difficult for him. Although not shown on screen, I think that when he tried the game again (alone in the room so he doesn't have to worry about what people are seeing) that he easily wins. And we never again see Bashir trying the game. It's too easy for him.
I think there are some retroactive reasons for why Bashir gloats a bit about significant medical events like reviving that dead guy in the beginning of "The Passenger" even though it would seem to draw undue attention to him (and he should be better at reading people and getting along with them):
(1) It really is a pretty impressive thing, and genetically enhanced or not, Bashir is young and wants to get some credit. Maybe a least part of him really wants the acknowledgment of his great deeds. Remember, Julian didn't know of his genetic enhancements until he was 15, plenty of time to develop a healthy arrogance about being better than everyone else. In fact, that's probably why his parents finally told him, so that he would tone down on the gloating and showing off (and tennis playing) so they wouldn't get found out.
(2) Maybe Bashir thinks that he can actually distract people away from the great dead (which might lead people to question his abilities) by gloating a little too much and therefore distracting people by having them think he's a annoying stuck-up know-it-all
Either way, it relies on Bashir being a very good judge of the people he talks with. Can you just imagine what his life is like, constantly having to lie to people and judge how they react to those lies?
I always thought it was weird in the early seasons how he was a bit of a ladies-man with women (like at the beginning of "Q-Less"), but everyone else thought he was a stuck-up kid they didn't want to hang out with, and he was always so clueless when it came to dealing with Garak. I think Bashir, even early on, is much more capable of being tactful in situations and controlling conversations the way he wants them to go. He would need to have honed those skills a little to keep his secret. But he almost purposely acts up a little too much (too annoying, or too proud, or too whimpy) to keep people off-kelter. In early seasons the only people he ever uses his full-blown conversation skills on are the women he dated. He is a young man after all, into sex as much as any other (as far as we get on TV). But I would/could also argue that Bashir is really still trying to find a balance. Still trying to know how much to lie and how much to reveal his true self. Remember, he didn't even know about his own genetic enhancement until he was 15. So his genetic enhancements couldn't really be all that much beyond regular people, or he would/could have been found out earlier. Maybe in these early seasons he really is what he seems, a brilliant young man trying to find a balance between pride in his work and modesty, while only occasionally worrying about getting "found out".
In "Q-Less" we learn that Bashir mistook a preganglionic fiber for a postganglionic nerve during the oral exam phase of his Starfleet Medical finals. Obviously any first year medical student would not likely mistake a preganglionic fiber for a postganglionic nerve. So it's likely that Bashir threw the question on purpose so that he would not be valedictorian. Maybe, like any person in that position, he just did it because he was nervous about being valedictorian and wanted to let someone else take the title. But maybe he threw the question on purpose because he thought the valedictorian title might lead to too much scrutiny. And he only needed the salutatorian title to get him the position he wanted out on the frontier. In fact, maybe he wanted to work out on the frontier because it kept him away from other doctors who might question his brilliance, something the "simple locals" wouldn't do as much (as stated in "Emissary"). Although some locals did see his brillance, like in "Babel", when Surmak Ren noted his great work.
In "The Passenger", maybe the only reason Rao Vantika's technique for imprinting his conscience onto a human brain was because it was Bashir's genetically engineered brain that already had a great sense of compartmentalization. And Rao Vantika noted that he really liked his "new body" when he was inside Bashir. Maybe he was noting Bashir's genetically enhanced abilities (without even really knowing that they were enhanced because he'd never been in a normal human body).
In "Move Along Home", I wonder what Bashir was actually going screaming in the game when Sisko, Kira, and Dax found him. Maybe his genetic enhancements allowed him to determine that he was actually in an artificial construct (which he couldn't share with his shipmates because he couldn't explain how he knew) and he was trying a technique to get himself out of the mental construct. He does say that he was "trying to wake himself up", which sounds like a ridiculous young man to the others, but may have been as truthful as he could let on at the time.
In "Armageddon Game", I wonder just how much Bashir actually knows about the subspace transceiver that he's not letting on the O'Brien. Ultimately it doesn't matter, however, because it's not repairable anyway.
Probably the Julian Bashir seen in all the mirror universe episodes was not genetically enhanced. I'm sure his parents, as slaves of the Alliance, couldn't afford the genetic enhancements that the regular universe parents could. Maybe that's why mirror Bashir seems so much stupider and mad at world. If you want to know how Jules Bashir would have turned out without the enhancements, you need look no further than mirror Bashir.
Perhaps Bashir's enhanced status was part of what enabled him to survive as a prisoner of the Dominion for over a month, as revealed in "In Purgatory's Shadow" and "By Inferno's Light".
Most of the episode "Distant Voices" plays out in Bashir's genetically enhanced mind. Perhaps the only reason Bashir was able to defeat Altovar's attack was because Bashir was enhanced. (I don't think a human NOT genetically enhanced could've or would've survived that Lethean's telepathic attack.) It's interesting how even though Altovar is inside Bashir's mind, he still doesn't fully understand Bashir's status as a genetically enhanced man in hiding. (This is similar to when Rao Vantika was inside Bashir's head in "The Passenger".) Altovar confronts Bashir about his past failures – the way he quit tennis to become a doctor because his parents would not approve, the way he intentionally missed a question so he would be second rather than first in his class because of the pressure. What was it Bashir's parents didn't approve about tennis? Did they not want Julian to squander the gifts that they presumably paid good hard-earned curency for? Or were they worried that the life of a super-star tennis play would make it more likely that his genetically engineered status would be found out? And, as has been previously discussed, Bashir probably threw that fiber/nerve question not just to avoid the pressure of being valedictorian, but the pressure of possibly be found out as enhanced (and therefore a bit of a cheat).
There was a little clue in the episode "HomeFront" about Bashir's past. Odo offered to check on Bashir's family on Earth and Bashir quickly put the idea to rest. Bashir didn't want to associate with his parents.
There's some interesting scenes in "Rivals" if you know Bashir's actual racketball skills are much higher than he normally let's on. First, Bashir has to pretend to be "normal" fit young guy, who can easily beat the older O'Brien, and then naturally gloat about it. Then, later in the episode, as the "luck game" starts acting on him, he finds himself loosing the game, even when he tries. How can this be? he may be asking himself; I'm much better than O'Brien, heck, I'm even much better than O'Brien thinks I am. Because I normally have to bring down my game so that no one recognizes my enhanced abilities.
But the scene I find the most interesting and revealing about genetically-enhanced Bashir in "Rivals" is not the beginning, when Bashir is winning, nor the end, when he's loosing because of the "luck game", it's in the middle, when Bashir "throws" the match to O'Brien because he feels bad for him. Remember, genetically enhanced Bashir is always "taking it easy" on those people he plays games with. He has to in order to not let on to people the fact that he has exceptional genetically engineered abilities. And he has also gotten very good at doing so in such a way that it appears natural, not like he's trying to loose. It has to appear as if he's trying to win, even though he's not really doing his genetically-engineered best. In fact, he often chooses to throw in some gloating and pride, maybe because he's just young and feels like gloating, but maybe because he's trying to throw others off the scent of thinking he's actually capable of doing even more than he's showing (and gloating about). But in the match he's trying to "throw" to O'Brien there is another interesting dynamic. He now has to pretend to have even less skill than he normally shows, which is already less than his real skill level. And you know that Bashir could have done so in a convincing way. He's had a lot of practice at throwing games in a convincing way. (Unless he has gotten SO use to his new "normal" level that this further-reduced level feels weird to him.) Yet in the episode, Bashir acts so obvious when he "throws" the game with O'Brien. When he's throwing a game, which he's probably done many times, he does so in a very obvious way. Was this just because he really didn't want to bring his game down so far? Or was he acting so poorly so that others couldn't possibly question that his normal level of play wasn't also faked? I'm not arguing one way or the other. I just think it's an interesting question to think about.
The absolute most interesting episode to rewatch knowing about Bashir's genetic enhancements, in my opinion, is "Our Man Bashir". Bashir, who leaves a real life as a multi-faceted man with secrets that he hides from everyone, wishes to escape into a place where he can really be himself and use his abilities to their fullest potential. Secret agent man program seems perfect. Interacting with a lot of different people using different personas (which allows him to hone his conversational skills, which are really a lot better than he lets on), high-speed mental calculations (with the right story), card counting, sharpshooting using his high hand-eye-coordination. So he sets up some free time to be with himself. Sets the program difficulty up really high so it's challenging. (Most people would set the program so that they win the card game without trying, but Bashir had it set up so that he had to card count a 5 deck set to do it, just to challenge himself, etc.) Then Garak shows up and Bashir has a dilemma. No problem, he thinks, I just get rid of Garak or secretly lower the difficulty level so that he doesn't see me doing these amazing things and getting too suspicious. But then the transporter/computer problems takes both of those choices away from him. So he's stuck having to continue with the program set at a risky high difficulty level to save his friends' lives, all why hiding his abilities from Garak . . . all while keeping Garak off-balance enough to not notice. It plays out really well. And Bashir comes across even more impressive when you view the episode this way. Especially at the end, when Julian shoots at Garak and it seems like Bashir was willing to shoot him, but the bullet didn't hit. In hindsight its obvious he intentionally missed as a warning and played it off like he meant to actually hit Garak (which, given his enhanced abilities, would have been easy).