Corrected entry: In one scene, Indy and the group are being held captive by the Russians and are being taken through a rain forest. After they hijack the truck that is transporting them, Indy destroys a deforesting machine with an RPG. The model of RPG that Indy fires wasn't invented until the 1960s.
Correction: Already listed and corrected. The RPG-7 was not invented until 1961, but the similar-looking RPG-2 was around at the time of the movie.
Twotall