The Hurt Locker
The Hurt Locker was released in 2009, but the story itself took place in 2004. The story follows soldiers who were out in the middle east as they try and figure out what their new leader is all about. In one scene, one of the soldiers offhandedly mentions Youtube. Funny enough, Youtube wouldn't have been invented yet as it was officially launched in 2005. This was a small fact that was overlooked, but many viewers noticed the discrepancy.
Gladiator
Gladiator didn't really care for historical accuracy in most parts of the film. Honestly, it was probably the least of their worries while writing the script. One fun fact is that Russell Crowe's character is nicknamed "The Spaniard" which is a word that was not around until the 14th century. The story was set in the year 180.