Stay Out Of The Basement (2) - S1-E13
Stupidity: When the real Dr. Brewer is found in the basement, he has duct tape over his mouth and needs his daughter to remove it for him. His hands are tied around the wrist, but not behind his back, so he could have easily removed the tape from his mouth himself long before he was found.
The Alternateville Horror - S4-E8
Stupidity: Colin tells the group he saw a ghost (a non-corporal shade) who walked through the door. They laugh at him and blame it on what he was watching on TV or too much sliding. Given everything the group has seen, vampires, a dragon, etc, they should have least checked it out. Quinn himself was once on the astral plane and nobody could see him except one girl who thought she was seeing a ghost, and he could walk through solid objects.
Stupidity: When Kellin is hit with the neurolytic emitter, it erases her memories of the outside world. However, the effects aren't immediate and take some time (enough to get her to sick bay and have time to talk to Chakotay). However, she spends her time telling Chakotay to help her remember their relationship, etc. when her memory is gone instead of just making a recording of herself describing the relationship and her feeling which can then be shown to her after her memory is gone. She might not believe the recording, but seeing herself discuss the situation would be better than just relying on Chakotay (who will soon be a stranger she never met) telling her something so unbelievable.