Continuity mistake: When the boys are trying to get away from the government agents on their bicycles, riding and maneuvering through their neighborhood, the stunt double for Elliot (extremely identifiable due to the red hooded sweatshirt) visibly wipes out. The next shot, meant to be continuous, shows Elliot upright and riding with the other boys.
Other mistake: While the kids are huddled around the kitchen table, Elliott is saying his lines, while Gertie is actually moving her lips, saying those same lines on the right side of the screen.
Continuity mistake: While Elliot and E.T. are saying goodbye to each other at the spaceship, you see Elliot's mom sink to her knees. Then, you see a close-up shot of Elliot and E.T. looking at each other and you can see her white shirt in the background as she gets back up, but in then there is a close up of her face as she gets up again.
Continuity mistake: The street the boys turn onto during the chase, when the boy says "we made it," isn't the same street as they had turned into. There should have been houses, but instead there were just trees and cars.
Revealing mistake: When the boys are racing away on their bicycles from the Feds, the stunt doubles for Elliott and his friends are obviously way too tall to be children.
Continuity mistake: When Mike and his friends are playing Dungeons and Dragons, Greg is on the phone requesting "Papa Oom Mow Mow." Towards the end of his call, Greg repeats the song's name twice. Look over Elliott's right shoulder in the next shot where he asks Steve's permission to join in: the phone is on the hook, but Greg is still talking to the DJ somehow.
Deliberate mistake: At the end of the film when E.T. is leaving, there is a bright light from the ship, and wind and dust from the spaceship's liftoff. But when the spaceship has lifted off and has flown into space and made a rainbow, they show Elliot and the others and there is still the shining light, plus wind and dust blowing for no reason.
Other mistake: This concerns the 2002-Version. For this version a lot of scenes have been changed/remastered digitally, e.g. E.T.'s mimic, the flapping of Elliot's coat during the bike flight, or some cloud movement during the night scenes. Even the guns were changed into walkie talkies. But every person who was holding a walkie talkie is still pointing out his trigger finger as if holding a gun.
Continuity mistake: When Gertie places a pot of wilting flowers onto the Radio Flyer wagon, an 'enter' sign can be seen on Elliott's bedroom door with a handwritten paper saying 'do not' taped upon it. After she knocks, Mike opens the door to let her in - but the 'do not' paper is now tucked behind the 'enter' sign instead.
Revealing mistake: When Elliot, Michael, and E.T. arrive at the park after escaping the scientists, a ramp can be seen where they drive over the curb.
Audio problem: When Mary is reading Peter Pan to Gertie, her shadow's lips don't match up with the words she is saying.
Continuity mistake: In the final scene of E.T., where E.T. is saying goodbye to Elliot, E.T. rubs Elliot's shoulders, then removes his hands from Elliot's shoulders. The shot then changes angles from behind Elliot to behind E.T. Upon changing the angle, E.T.'s hands can be seen back on Elliot's shoulder. When the shot alternates between the two angles (for about ten seconds) so does E.T.'s hands alternate being on or off of Elliot's shoulders.