Factual error: In the scene where Forrest gets his discharge papers, he is practicing table tennis in a gym. The gym floor has a three-point line on the basketball court. It is a college or high school three point line- 19 feet, 9 inches. There was no three pointer in basketball at that time, especially at that distance.
Other mistake: Forrest begins his run across America the day President Carter collapses in Maryland. This is October 1, 1979. When he stops running, he says: 'I had run for three years, two months, fourteen days, and sixteen hours.' Some time later, he gets Jenny's letter - the day President Reagan is attacked. This is March 30, 1981. So, he only ran for one and a half years.
Continuity mistake: In the scene where Forrest is getting on the school bus for his first day at school, he is standing at the door talking to Dorothy Harris, the bus driver. The shot from behind Forrest shows Dorothy's right hand on the gear shift knob. In the next shot, from inside the bus looking down at Forrest, her right hand is on the door-open lever. This shot changes several times, and each time her right hand is in those two different positions.
Factual error: In the scene where Forrest's platoon is crouched down along the side of the road, and the narration is introducing some of the soldiers, you can see a pack of Marlboro cigarettes in one of the men's helmets. On the side of the pack is, "Marlboro Miles." These weren't available until the 1990's.
Continuity mistake: During Forrest's first football game, he is standing staring off into space when they receive the kickoff, his teammate runs over to him, hands him the ball, and tells him to run. Forrest says, "Okay". The camera cuts to the coach on the sideline who is yelling for him to "run!, run!", while at the same time his head is turning as if he is watching Forrest run past him. The next camera shot shows Forrest running, but he has not yet gotten to the point on the sideline where the coach and the team are standing.
Continuity mistake: When Forrest sees Jenny at the anti-war demonstration in Washington D.C. he runs through the crowd towards the pond. We see that the gap between the people who let him through closes immediately after him, but in the last shot it remains wide open, obviously to allow a more dramatic view of Jenny's and Forrest's reunion. However, when the crowd is shown from the other side there's no gap at all.
Factual error: In the scene where Forrest Gump is wheeling Lt. Dan across a street between a bunch of taxis, the car they go behind is a 1973 Chevrolet Caprice (see the tail lights). However, several scenes later we know the year is 1971 because it is New Year's Eve 1971 because we see the TV flash 1972 as the year changes.