Factual error: When Forrest is talking to Jenny at her grave, he says "You died on a Saturday morning." But 22 March 1982 (the date on the grave) was a Monday. (02:04:05)
Factual error: We've already seen George Wallace on the school steps in one of the scenes where Forest is inserted into the footage, and this happened in June of 1963. Then it shows an All-American team meeting with JFK but that was created in December. But there was no way JFK would have been there as he was assassinated the previous month.
Continuity mistake: In the scene where Forrest is attacked by boys who are throwing stones he is hit underneath his right eye. In the next shot you can see Forrest bleeding from a wound on his forehead.
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.