This may sound like an odd thing to ask. I myself like most incarnations of Star Trek, but there are certain "Star Trek-isms" that occasionally annoy me. A lot of them come from my experiences in an actual navy onboard a submarine. Not the same thing, so I can't say the Trek-isms are "incorrect" or "wrong" but they do annoy me.
The first one that always bugs me is officers reminiscing about their days at the Academy. You can tell these lines weren't written by anyone who actually attended Annapolis or West Point. Chakotay and Janeway walking down a passageway sharing Academy stories relevant to the plot of the episode they are in. "I remember so-and-so, my instructor in warp mechanics at the Academy..." They look back fondly as though Starfleet Academy is a civilian college where fun is had rather than the kind of grueling, disciplined place of academic hardship that an officer academy is. Naval officers do NOT reminisce about their days as cadets. They do, however, reminisce about previous commands they've worked at.
Anybody else?