Incorrectly orientated boards and swapped K and Q are so commonly seen on film that they are not hugely interesting. But here's an example anyway - the official video for a Madonna song. I thought it's cute because not only did it have the first error but it also showed Black moving first. See 0:42 and 1:30.
Recently I saw an advertisement (can't remember what the ad was about) that shows a capture of a king (the player knocks over the opposite king while holding his piece). All I can think of is "nobody there knows how to play chess"!
In the gun forums, there are a lot of posts about how hollywood incorrectly used guns. For example, in Rambo (I saw this many years ago, so it may be another movie), where the bad guy holds a gun to Rambo's neck (who's tied up) threatening to shoot him. Unfortunately, the semi-auto pistol slide was locked back (and I'm sure Rambo being so knowledgeable knows that it won't fire). so that was funny. Then there's the needless slide racks on pistols in so many films.
So how about chess?