Audio problem: During the football match when Forrest runs and bumps into the band players, we hear what sounds like cymbals crashing/dropping to the ground. But if you look at the band players he knocks over, there are no cymbals anywhere near them.
Audio problem: John Lennon's lips don't sync with what he's saying. Neither do Kennedy's or Johnson's or Nixon's.
Audio problem: In the shot that shows Forrest punch a man three times, there's problems with the sound effects. The first punch has no sound. The other two are too late, they appear after the punch.
Answer: It's not specified in the film, but in the sequel book "Gump & Co" the author mentions that Jenny dies from Hepatitis C as a former drug addict in the early 70s. Hepatitis C was an unknown disease until 1989.