For some reason now that you mention this I'm thinking I remember the beginning of Temple of Doom it gives the date as being 1938 whereas in Raiders it gives the date as being 1939..........
I could be way off on this......havn't watched the movies in a few months.......but that's what's popping into my head right now.
Oh.....and the reason for this is quite simple.
Temple of Doom was a completely different story with different characters (except for Indy). By setting the movie BEFORE Raiders, they did not need to tie up the loose ends with the characters at the end of Raiders. They did not need to rehash what had happened to the characters and how Indy came into contact with new characters like Short Round.
by the way......it's not a continuity error. it is simply a call back to a previous movie. Who ever said that in Raiders when Indy shoots the swordman with his gun that was the first time he had ever done it. That's like saying playing Darth Vader's theme in Episode II when Anakin slaughters the Tuskens is a continuity error.
A continuity error means that there is an error in the order in which events happened.