I have found that every episode has its "that can't happen" moment. I just take it as one of those things we must accept because it's fiction. From the obvious "according to science, no one could possibly travel beyond the speed of light" (I do like the inventive idea of a warp field as a solution to this, and scientists can be a bunch of party poopers)), to the wide-spread, long-time quandary of..."If a person who is out of phase.. or a ghost...any being who can pass through walls and bulkheads, how is it that the floor will support them?" [The next Phase]. As Captain Picard quipped and we see him laughing for the first time: "Sometimes, Number One, you just have to bow to the absurd" [Up The Long Ladder] (I love this episode: Picard has been discovered to have a sense of humor..though he doesn't really show it, and Doctor Pulaski and Worf are developing a strong bond as well as introducing the romantic and poetic mind of the Klingon. Unfortunately, Doctor Pulaski's character-development came too little, too late.)
However, I do know what you are talking about. Sometimes there is "the reach too far". We are going along with the story and enjoying the journey, then something happens that violently yanks us out of the tale and brings us, unceremoniously, back to our living rooms. We allow the writers and the directors our faith to take us by the hand and lead us into a world of fiction. It's like reading a period novel and the major protagonist starts chatting away in modern-day grammar and jargon (Like "I'm sorry for your loss." which happens quite a bit in current day self-publication. That phrase started being used in common language in the late 1970s not the 1870s)
Back to Star Trek, this doesn't happen as often for me, most likely because the story is in the future. They do have a bunch of wiggle-room. Hmmmm, I'll have to think about this. Let me get back to you.
Ah I do have a problem with Troi's caution when they meet people for the first time "Be careful, Captain. He's hiding something". Well, duh. EVERYONE, when they first meet, are hiding something. If she could extrapolate, it would be very helpful....like "he's hiding something that will do you harm." or "he's planning to manipulate you".