I understand the general concept of copyright in terms of using others' music, but is there any kind of problem I may run into by showing characters watch a clip of a movie or tv show in my film?
I don't think you do understand the general concept of copyright. Copyright does not exist specifically to protect music, it exists to protect Intellectual Property (IP) in general and music composition, arrangement and recording are just 3 of the many types of IP. Movies and TV shows also obviously contain various types of IP and are therefore covered by the same copyright laws as music.
If you make money off it. possibly ... i doubt people will come knocking at his door over twin peaks
It's a common fallacy that copyright laws are only broken if one profits/makes money from from it. This is patently incorrect!! As the term suggests, copyright law exists to protect the holder's exclusive "right to copy" their own intellectual property. So if you use/copy (even unwittingly) someone else's intellectual property without the IP holder/s written permission, then you have broken copyright law, period (there is a "fair use" exception but it is not applicable in this situation). Profiting/Making money from effectively stealing someone else's IP determines/affects the amount of damages the IP holder can sue you for, it doesn't determine whether or not you've broken copyright law! In the case of an amateur filmmaker at a regional film festival, it's unlikely the IP holder would find out about the copyright infringement and even if they did, with no profit involved, it's unlikely they would go any further than issuing a some sort of take down notice/injunction. So you're correct in doubting anyone "will come knocking on his door".
However, you're missing a vital point! When a festival screens your film/short, they too are covered by copyright law, which is why every festival will require you to sign a document/disclaimer stating that you are the IP holder and/or have all the necessary IP clearances. Even with this disclaimer though, no self respecting festival is going to risk being shut down or sued, so as soon as they notice an obviously unauthorised copyright infringement while evaluating the submissions, your film will be thrown straight on the "reject" pile.
Your advice is terrible, not just because you are basically telling the OP not to worry about breaking copyright law but also because all his work/effort in making his film will be wasted when every festival he enters will/should automatically reject it!
To the OP: Take Alcove's advice and try to think of some way to imply your characters are watching Twin Peaks without actually using any Twin Peaks sound or footage.
G
