Continuity mistake: At the beginning of the movie, before meeting Jenny, Forrest is sitting on a bus bench wearing the Nike shoes he received from Jenny and ran across the country in. When he arrives at Jenny's and crouches down to meet little Forrest, he's wearing brown loafers.
Continuity mistake: When Forrest gets hit by a stone and falls on the ground a red school book is lying on the ground next to him. When he gets up he doesn't pick it up, and when he runs away it's not on the ground either. (00:15:20)