Continuity mistake: In the scene where Forrest goes and visits Jenny (and is introduced to his son), there is an iron on the ironing board in the background. It stands up, then down, then up. The child's artwork in the background also disappears. (01:56:25)
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.