Continuity mistake: In the scene where Lt. Dan is waiting on Forrest at the dock, and Forrest jumps overboard off his boat to swim over to meet him, Forrest's hair and face are mysteriously dry for him to have just come out of the water, as if he towelled off his head before climbing the steps up to the platform.
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.
Continuity mistake: Young Forrest's foot gets trapped in a sewer with a bunch of leaves around. When the angle changes the leaves are gone.
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.
Continuity mistake: The first time that Forrest runs across the football field, a front view of the coach's head shows him following Forrest without moving his head, coach just moves his eyes. But a back view of the coach's head shows the head moving, following Forrest's movement. Back to the front view and the head is still. (00:20:30)
Deliberate mistake: In the scene where Forrest is describing his heritage, the clip of KKK on horses is taken from The Birth of a Nation. In this clip, you can see tire tracks on the dirt road well before automobiles were supposed to be in existence. Robert Zemeckis decided to leave this mistake in to perfectly match the clip to the original movie.
Continuity mistake: When Forrest sees Lt. Dan again after buying the shrimp boat, he dives off the boat and you see the boat going to the right, but after chatting for a short while they see the boat going in the opposite direction and crash into the pier. Even if it somehow turned itself around, it would would take longer than that.
Continuity mistake: When Forrest lifts Lt. Dan to carry him out of the jungle, there is a pack slung over Lt. Dan's left shoulder. When the shot changes to Forrest carrying him over his shoulder the pack has disappeared, without time for it to have fallen off. Notice, this pack is separate from Lt. Dan's large field pack, which Forrest does unbuckle before he lifts him onto his shoulder.
Continuity mistake: When Lt. Dan gets lifted off the bed by the male nurse, the handle he was holding on to disappears when the camera cuts to Forrest - it was so low that it should be in the picture. (00:55:30)
Factual error: In the scene where Jenny is snorting coke, "Get Down Tonight" was playing, which came out in 1975. Then we cut to Hurricane Carmen, which hit in 1974. (02:25:00)
Continuity mistake: In the scene just after Jenny shows up while Forrest is mowing his yard, Forrest and Jenny are walking and they happen upon Jenny's old house, where she lived with her father. She starts out by throwing her shoes, which she is carrying in her hand, at the house. The shot changes to view her from behind as she is throwing rocks, and she is standing on or just in front of a patch of grass in the driveway. As the shots change from in front to behind her, her position in the driveway has moved back from her original position, which is farther from the house by several feet, and when she finally collapses to the ground in tears, the patches of grass in the driveway have disappeared.
Continuity mistake: When young Forrest goes to young Jenny's house and he finds her in the backyard, they run away from the back of the house to get away from her drunken father. They kneel down in a patch of corn and pray to turn into birds and fly away. The camera then pans up over the corn and you can see that they are in the corn field in front and just to the side of the house, not the back of the house. (00:17:35)
Continuity mistake: After Forrest gets his medal he meets Jenny at the anti-war demonstration. When she goes to the bus to leave they are standing talking. In one shot his medal is tucked inside his jacket, but in the next shot (right before he takes his medal off) it is on the outside of his jacket. (01:09:15)
Continuity mistake: When the platoon is walking down the trail and he says they are always looking for a man named Charlie, he has a pack of matches in his helmet from his rations. When they get on their feet, he has a pack of napkins next to the matches. (00:44:15)
Factual error: When Forrest is reading the letter from Apple Computer, Inc., the date at the top of the letter says September 23, 1975. However, Apple wasn't founded until April 1, 1976 and wasn't incorporated until January 1977. No way to get a letter from a company that doesn't even exist yet.
Continuity mistake: When Forrest stops running, the close-up on him shows a sunny road with no painted lines on. The rest of the angles are of a shadowy place with painted yellow lines. (01:53:10)
Continuity mistake: When the school principal shows the poster with the IQ requirements for regular schooling to Forrest's mother, the grip on his pencil changes back and forth in shots from the front and from behind. (00:07:50)
Continuity mistake: Before young Forrest's foot gets trapped in the sewer, a black car in the back is moving towards him, and is about to make a right turn. Close-up on Forrest's foot and, when back to the wide angle, the same black car is further back again and repeats the previous movements.
Continuity mistake: The first shot from above with the floating feather is mostly overcast. Shortly afterwards, after the feather lands and the lady walks up, the sun is coming from the left into the plaza.
Continuity mistake: Young Forrest is about to step in the bus. He says to the bus driver, "My name's Forrest, Forrest Gump." That moment we have a back view of the bus driver's head and she exhales a big puff of smoke. A split second after we cut back to a front view of her and there's no smoke, instead she immediately exhales the smoke again.
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.