For me:
The worst part of the Treknobabble™ isn’t that it’s there and that it sounds silly, it’s that the Treknobabble™ is what RESOLVES the plot.
Transporters and replicators - almost every damned episode they have to come up with some BS reason as to why they’re not working…even though there’s no reason they CAN’T just use it to solve the problem.
Holodeck crap. I don’t mean the obvious stuff, but some of the non-obvious stuff. For example, there was a not-so-terrible episode of Voyager where the crew found a program that was a “what-if” scenario involving a mutiny on the ship. Instead of actually, you know, doing some good writing and using the setup to have a nice character-driven episode. Instead, of course, it becomes a “the holodeck is taken over by a sleeper program and it’s going to blow up the ship” episode.
Oh look, it’s this series’ version of the “alien/droid/sludgelump that wants to become more human”, because, apparently, becoming more human is the overriding goal of every species out there. Every series needs one of those…
I didn’t hate it, but boy ol’ God did I feel sorry for Riker. They spent, what, seven seasons trying to give him a personality? Failed every time. Ooh! He plays the trombone! Yay!
The fact that nobody bothers using a phaser like a fucking firehose to take out an entire enemy platoon.
All of the “don’t shoot me, he’s the evil double, shoot him!” moments…when your gun has a STUN setting. Shoot them both and work it out later.
Continuing the technology bitching…remember in DS9 when they had to give up the station to the bad guys? I remember that Rom created a bunch of space mines to make things harder on the bad guys. But not only were these Space Mines, but they were Replicating Space Mines so that when one blew it would recreate itself. Idiotic.
How about the fact that you can transport an away team to an enemy ship, borg cube, or whatever, but for some reason you can’t just transport over a big ol’ block of antimatter.
A fantastic lack of continuity. You can’t transport through deflector shields. However, theres these armbands that let you transport through shields, but they will eventually, after long usage, cause cancer. So the good guys don’t use them. Of course, there’s hundreds of occasions where having such armbands around would allow you to save EVERY LIFE ON THE CREW…but for some reason we can’t just keep a couple of these things in storage for emergencies.
The Prime Directive. The biggest load of plot device ever shat out upon television.
Oh, and that I seem to be the only person who thinks there’s a major similarity in looks between Chakotay and Bill Clinton.
That’s my short list.
-Joe