There's a lot of clips and conversations about what the writers got wrong in terms of continuity they got wrong. I think there's like a 10 minute Youtube thing on blunders the writers made in terms of the almighty "canon". Well, in non of these converstations do I ever hear what the writers got right. So I beg the question, What pieces of continuity did the writers get right. Any show/movie is fair game, and the smaller it is, the better, and heck, it makes us look smarter. I guess the example I'm looking for, the reason I bring this up would be something like this: How Guinan met Picard, from telling the story in Booby Trap to the series actually showing it in Times Arrow. You'd think after watching the former that something like that is miniscule to the overall point of the show, but when they actually bring it up again later on and actually show it, well, it was the last thing of TNG (After watching it many times) I found that was new and I thought it was incredibly awesome.
I kind of liked how the description of first contact with the Vulcans in Voyager was right on to what they showed in the film First Contact. I know this was really done on purpose, and the portrayal of Cochrane was rather more like that film than Metamorphosis in TOS, but still, I liked the continuity. And since that's the most recent Trek I've seen, it's fresh in my mind. I also liked some of the little references to earlier people, such as the Daystrom Institute's reference to Richard Daystrom from TOS Ultimate Computer.
I liked how in DS9: In the Pale Moonlight, they referenced how Vulcan, Andoria, and Tellar were all relatively close to Earth. They later showed this in ENT, especially the episode Home, where they say that Vulcan is only sixteen light years from Earth.
The fun thing about Star Trek is that overall they got most of the things right. Which is why all the claims about canon and continuity exist to begin with. Otherwise nobody would have been able to create books like The Star Trek Chronology or Encyclopedia, and sites like Memory Alpha wouldn't exist. If Star Trek was all about ignoring stuff, nobody would ever be able to bitch about continuity errors. But I'd say that like 90% to 95% of the canon is totally in line with continuity. That is why small errors stick out like a sore thumb.
DS9 episode Destiny, a Bajoran vedek tells Sisko his final trial will involve fire, or something like that. And then in WYLB, Sisko and Dukat have their big showdown in the Fire Caves.
I love the really obscure bits of continuity. Such as the entity Onaya name-dropping the writer/poet Tarbolde in The Muse (DS9). Tarbolde was originally mentioned in Where No Man Has Gone Before when Dr. Dehner askes Gary Mitchell to quote from one of his works. I also loved the mention of the Hur'q invasion in ENT's Affliction.
Neelix lost a lung early in the VOY run and think they continued to reference that throughout the series.
The DS9 episode "Trials and Tribble-ations", which revisted TOS Season 2 episode "The Trouble with Tribbles" with the DS9 characters and had Ben Sisko, Miles O'Brien and Dr. Bashir interact with Captain Kirk "Forrest Gump" style. It was a 30th anniversay of TOS tribute episode. We even got to see Captain Koloth's Drell 7 Class Klingon Battlecruiser orbiting the Federation Space Station K-7 while the Enterprise was orbiting it as well. Something that was not in the TOS episode. I know, I know, the Klingon Battlecruiser was not seen until TOS Season 3. Navigator NCC-2120 USS Entente /\
The problem is, nobody does, although it's the truth. Most people say "Star Trek was inconsistent all the time!" but that's basically just wrong.