Back to the Future
Back to the Future should have really been called Guitar from the Future. At the end of the film, Marty McFly has successfully united his parents at the 1955 prom to verify his own existence, and he soon takes the stage to shred it on the guitar in celebration. All's well and good, except for the fact that McFly is playing a Gibson ES-345, which didn't exist until 1958.
Bernie
This 2011 Richard Linklater film tells the store of millionaire Marjorie Nugent's murder in 1996. Although the majority of the narrative adheres to true events, Linklater decided that iPhones were to be used throughout the film. Strange, considering iPhones didn't even exist until 2007.