Why didn't the doors open for Spock resulting in his falling into the corridor?
The ship's internal sensors could tell that if the doors opened, Spock would be off-balance, whereas Riley would not be, so they opened for Riley's convenience, but stayed closed to keep Spock on his feet.
Troi can tell when you're bluffing but I bet I could still kick her butt at poker. <snip> Speaking of which, why do people in Trek always play 5 card stud? <snip>
And why do all the militaries of the world do their fighting with huge, fragile ships that are bad at maneuvering? Babylon 5 and Battlestar Galactica both had fighters, because they make so much more sense.
Troi would be able to tell you think she's a sucker, too. And by the late 23rd century, 5 card stud and Fizzbin are the games to play.

And if you want to get into combat tactics, why do they even allow the crew to be involved beyond saying "attack" at all? A computer's response times would be insanely faster.
Why do starship databases contain such useless information? For example, in Flashback Janeway accesses logs from the Excelsior consisting of Sulu noting "routine maintenance" being done.
1) Wouldn't it make more sense for the ship's computers to access that from Memory Alpha or whatever?
2) Why is "routine maintenance" even considered interesting enough to be saved for 80 years?
Memory Alpha might not always be available. And in a world where information is stored digitally and can be changed even retroactively with near zero effort, having copies of the information all over the place is a strategy for keeping the record HONEST - this is a problem we are dealing with NOW, in fact.
Jean Luc Picard is from France. Patrick Stewart is from the UK. He speaks a crisp English accent and never bothers to speak in a French accent except minimally on one occasion.
Why? Why not make him from England and in keeping with his accent as he doesn't seem able to lose it?
If English is "Standard", and it seems to be, then it seems logical to me that, much like the way well-educated Indian speakers have a British accent now, so would it be for most of Standard-speaking Eurasia.
My imponderable: Why is every single admiral in Trek either grossly incompetent or someone who would rather be a captain again?
Being on a ship gets you out away from the regime back on Earth, and there are some disturbing things about the way things are run on the Federation homeworlds. DS9 gave us a peek at that, but if you consider the implications of all the tech and social dogma we've seen, it would pretty much HAVE to be even worse than we know from screen canon.
I guess that means depriving oneself of emotions automatically makes one arrogant. If so, that's illogical as arrogance might be considered an emotion.
...or it could be simply bad acting. Watch Surak sometime in the TOS series episode The Savage Curtain.
Surak came to the conclusions on his own. His early adherents were probably enthusiastic, too. But once it had time to become dogmatic, there's probably a lot of Vulcans who are caught between thinking it is the proper way to live and simultaneously resenting the hell out of it.
How come when Worf throws a Klingon word into the conversation (or when any alien character speaks their own language) the universal translator doesn't translate it?
Comm system and translator AI beyond anything we have now - perhaps it picks up on his speech pattern to clue it in, or per another haps, it determines this by the fact that Worf is normally speaking unbroken Standard, so if he has thrown a Klingon word in, he has obviously done it on purpose.
Why do they sometimes have to press their commbadges in TNG but other times just talking into the air suffices?
The same AI I just mentioned is pretty good at picking up on vocal and somatic clues as part of its UI. But not perfect, and also, sometimes people just like to fondle their brooch.
