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.
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: 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: 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.
Continuity mistake: During College, when Forrest first visits Jenny in her "all girls school". Jenny shows her breasts to Forrest and lets him touch her. When she hurries and puts on her bra, her right bra strap is twisted. When the camera pans away the bra strap is straight again.
Continuity mistake: When Forrest and Bubba meet Lieutenant Dan for the very first time the sun changes between shots.
Continuity mistake: In Washington, when Forrest runs to meet with Jenny he runs between the same people twice. Check the man on the right with the black top hat and a violet ribbon.
Continuity mistake: When Forrest comes home after being discharged from the army, his mother greets him outside and it's overcast. The shadows on the ground are very faint. But in the shot from inside the house, it's suddenly sunny outside and the shadows are very dark.
Continuity mistake: In the scene where Lt. Dan thanks Forrest for saving his life and "makes his peace with God", before he jumps overboard off the shrimp boat, the water is flat calm. In the next shot when he does jump and is doing the backstroke, the water is slightly choppy or rippled.
Continuity mistake: When Lieutenant Dan arrives to be Forrest's first mate, the shot facing Dan shows Forrest stepping onto the boat's ledge with his left leg, but in the very next shot facing Forrest he is suddenly using his right leg.
Continuity mistake: When Forrest Gump stops running, the road has paved shoulders. In the close-up, the shoulders are all weeds.
Continuity mistake: When Lt. Dan shows up to be Forrest's first mate, he is smoking a cigar. From one angle the cigar has more ash than the next.
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.