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.
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.
Continuity mistake: When Elliot's mother is retrieving a heavy blanket to put over him because he is faking an illness, she tears open the closet doors and the leading edges of both doors come free from their tracks. A moment later when the shot angle changes, and you see her from inside of the closet, both doors are open, but both are back on their tracks.
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.
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.
Factual error: The government operatives go to great lengths to cordon-off and sanitize Elliott's home with extensive hazardous material preparation. Controlled airflow, Hazmat suits and everything. But as soon as E.T. "dies," everybody takes off their Hazmat masks. So, E.T. was only a Hazmat threat when he was alive? A real government Hazmat team would never drop their guard like this, as long as the alien body was still present.
Visible crew/equipment: When Elliot is luring ET with Reeces Pieces and goes into his room and through his drawers to find more candy, you can see the shadow of the crew moving on the wall next to Elliot.