Pirates of the Caribbean: Curse of the Black Pearl (2003)
The first installment of the Pirates of the Caribbean saga had one minor flaw. When Captain Jack arrives at Port Royal, the British soldiers holding him at gunpoint are wearing red coats. The British Empire didn't issue these uniforms until 1747, but the movie takes place in the 1720s.
Public Enemies (2009)
Johnny Depp plays John Dillinger in Public Enemies, a charming bank robber in Depression-era America who J. Edgar Hoover and the newly-formed FBI considered a pest. Here, Dillinger can be seen wearing a modern, sleek robe that no one would have been able to afford at the time, nor would they have worn it in the first place.