Revealing mistake: During the scene in the woods with the communication machine, Elliot tells E.T. that they need to go. You see the machine still working at a regular interval because a rope is pulling it. The shot pans to the left a touch and the rope stops moving, as if the person pulling it realises it's no longer in the shot.
Revealing mistake: The silhouette of the mime wearing the E.T. gloves can be seen through the railing when Elliot is luring E.T. with the Reese's Pieces.
Revealing mistake: In the opening chase scene where E.T. is running back to the ship you can see the cart that E.T. is on when it is the side shot of E.T. and to left there is a gap in the plants and you see part of the cart.