Argo (2012)

Beyond Ben Affleck’s white-washed casting as Tony Mendez, his 2012 Oscar-winning film is mostly true to the story save for its depiction of how their operation was selected. Mendez's plan to pose as a Hollywood producer doing location scouting in Iran was one of three plans put forth in the effort to rescue six Americans during the hostage crisis in 1979. Of those three plans, Mendez's was actually the one that received the most support, contrary to how it's depicted in the film. Granted, there would be less tension if that wasn't the case, but it is a detail that arguably changes things up dramatically.