Independence Day

The last thing that anyone is worried about during an alien invasion is how realistic a shot can be, but a bunch of fans noticed that this scene was a little off! This is an image of the Empire State Building, but everyone knows that the actual shot is impossible. The real Empire State Building is set on a street corner, so it's impossible to have it perfectly centered. 

Braveheart

This is a pretty well-known downfall of Braveheart, but people still love to point it out. The film was set in the year 1300 and followed a Scottish patriot who famously led a revolt against the English army. Since he was Scottish, the main character was commonly dressed in a kilt. The folks behind the scenes must not have been paying attention to detail since kilts were actually introduced in the 16th Century, an entire 200 years after this film was set. The kilt must have been too good to pass up!