Here's one of mine. Star Trek (TNG and Voyager especially) seems to suffer from it a lot but I've seen it in other shows too.
The episode starts. Everything is normal. Then one character on board the ship hears voices/sees something or something that isn't there/notices something strange that goes away as soon as he looks away.
Character shakes his/her head and goes about his daily business until it happens again. This happens 3-4 times before the character bothers to say anything other than "Did you just see something?"
What annoys me is that after 10-20 different situations that have nearly resulted in the destruction of the Enterprise or the loss of crew no one ever thinks to post a standing order saying that "all anomalous sightings MUST BE REPORTED IMMEDIATELY!"
I've seen cases of this in other shows so I'm not specifically having a go at Trek but Trek is the best example of it happening. To be fair I recently saw an episode of Enterprise (3x06 - Exile) where Hoshi did exactly the right thing. She reported the problem on every single occurence giving as much detail as she could. Unfortunately the rest of the crew were too stupid to believe her at first.