Revealing mistake: When Forrest finally catches shrimp on the boat, the net drops shrimp on the deck which are not only already dead, they're headless and very obviously processed for shipment to market. (01:32:30)
Revealing mistake: In the scene where Lt. Dan chases the hookers out of his apartment, if you look closely at how he's carrying himself you can see Sinise use his real leg (which was then hidden by the special effects people) to push himself back into his wheelchair.
Revealing mistake: While Forrest is playing the Chinese ping pong player, the camera shows him returning powerful volleys with ease. During one of these returns, his hand and arm bend at an unnatural angle due to the CGI graphics changing a forehand shot to a backhand shot.
Revealing mistake: In the black-and-white newsreel footage of Forrest's All American team visiting President Kennedy in the White House, Kennedy is handling a football and you can see to the right of his grip "N STATE" printed on the ball and beneath that the signature "Rip Engle." The producers obviously spliced stock footage of when the Penn State team visited the White House following their Gator Bowl win in 1962. Rip Engle was their coach at the time. (Kennedy's hand hides the first three letters of Penn State).
Revealing mistake: When Forrest is playing ping pong in the gym and an officer comes to give him his discharge papers, Forrest reaches for his paddle and the ball but when he picks up his hand, there is no ball although he is acting as if there were. The ping pong scenes used CGI to put the balls into the scenes and this was obviously overlooked.
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.