When im watching movies or playing fps games i look for errors of how various firearms are described, depicted and how they are operated. I also usually point out these errors to anyone who is also watching/playing.
Most of the firearms mistakes that make me cringe at least in films, have already been posted id like add these game related ones.
many games devs do not understand how a belt fed machine gun works or are just too lazy/cheap to create the animation, but i noticed i many fps games, that after i have fired off the last of my ammo belt, there is still an ammo belt hanging from the side of my gun,and it is pulled away in the reload animation. wrong. in a select few games, you can watch the last few rounds of an Mg belt being pulled into the gun, just like in real life. Use a belt fed MG in any recent CoD or BC2 and you'll see what i mean. Hopefully the animation is correct in BF3.
another common error is the reload animations with magazine fed weapons. BC2 made lots of errors here. For example, the AK, when loading from empty, after a new magazine is inserted, the charging handle must be pulled back and released to chamber a round. this dosent happen, so in real life the weapon would not be able to fire as there is no round in the chamber. This is repeated with the G3, and most other assault rifles in that game.
A little attention to detail, and some research on how various firearms function would greatly benefit the video game and film industry and lead to more realistic representations of real weapons in games and films.