Captain America: The First Avenger (2011)
In the first installment of the Captain America franchise, Peggy Carter, Cap's love interest, is depicted with a shoulder-length hairstyle. Although her hair does appear to fit the fashion of that era, women serving in the military during the 1940s had to tie their hair back; it wasn't allowed to touch the collar of their uniform.
Back to the Future
In the pivotal school dance scene, Marty McFly (Michael J. Fox) is jamming out on the guitar—which happens to be an ES-345 Gibson from 1958. However, McFly wouldn't be able to have played "Johnny B. Goode," because he was transported back to 1955.