Catch Me If You Can (2002)
This 2002 crime film, featuring Leonardo DiCaprio, Amy Adams, and Tom Hanks, was supposed to take place in the 1960s. Adams can be seen here wearing wire metal braces, but that type of dental wear didn't become popularized until the 1970s.
Good Night and Good Luck (2005)
The historical drama Good Night and Good Luck, about a conflict between a veteran television reporter and a U.S. senator, stars David Strathairn, George Clooney, and Robert Downey Jr. Set in the 1950s, the film features officers wearing name tags. However, name tags like this would not have been worn by military personnel until 1967.