While I never got a chance to mention this in class, I still think this was a nifty thought. During my viewing of the film, I was really impressed with the way Zemeckis and his visual team meshed Tom Hanks into already established events and film. It reminded me of an episode from Star Trek: Deep Space Nine called Trials and Tribulations.
The episode involved Captain Sisko and his crew being thrown back in time by a prisoner they were taking back to Earth. They were zapped back into the time period in which Captain James Kirk and the crew of the U.S.S. Enterprise were still out and about in the galaxy. Turns out, they exposed the priosner a long time ago and he wants revenge. In order to stop him, Sisko and his crew need to "blend in" with the Enterprise crew and the people on the space station the Enterprise is visiting, all the while trying their best not to screw up the established time line.
The crew is shot back to the events taking place in the Original Series episode "The Trouble With Tribbles" and with the exception of spiffing up the visual on the 1960's ships, the cast of DS9 had to be superimposed into the footage in order to keep in check the fact that they were interacting around the original Enterprise crew. The best of these scenes is the finale, when Sisko breaks protocol, for unharmful fun, so he can hand the next day's duty roster over to Kirk on the bridge of the Enterprise. Just like Forrest speaking with any one of the three presidents he met, it was pulled off very well, almost like an actual conversation between two generations.
If your a big fan of Star Trek, or the visual style of Forrest Gump, I highly recommend this episode "Trials and Tribulations". for your viewing pleasure.