Continuity mistake: When Elliott finds ET hiding behind the stuffed animals in his closet, Elliott's holding two plates in his hands while balancing two cans of Coke on his forearms, then one of the cans falls over onto the plate, but in the next shot we can see that can under the plate and it's upright.
Continuity mistake: After Elliott finds ET all dressed up courtesy of Gertie, when ET heads into Elliott's bedroom the large oval striped rug has its center under Elliott's bunk-bed, but when they're all in Elliott's room that rug is pulled out (which can't easily happen due to the weight of the bunk-bed) and now covers much more of the floor area, between the bunk-bed and closet.
Other mistake: While ET is pulling the blanket loaded down with small appliances, etc., the TV is playing "Francis Goes to the Races" and when the film's Peter and Frances walk into the stall we hear Frances (the woman, not the mule Francis) say, "Grandpa, what's wrong?" but the subtitles on the DVD (1982 and 2002 versions) read, "Stanford, what's wrong?" and the subtitles on Netflix (1982 version) read, "Francis, what's wrong?" Additionally, when ET pulls the blanket behind the TV, on the TV screen we see Frances join her grandfather and we hear their dialogue, but in the next shot as ET stumbles out from behind the TV very drunk, even though we hear the TV's continued dialogue, what we actually see on the TV screen is a repeat of Frances joining her grandfather again, and then it jumps to the scene of Peter in the stall with Francis.
Continuity mistake: When Mary sees ET lying on the floor in the bathroom, in the closeups of Gertie there's a white fringed hand towel hanging on the rod behind her, but in the wideshots that towel isn't on the rod though we see a small white towel lying on the counter when Michael picks her up. Then in the following shots of ET the white fringed hand towel is hanging at the end of the rod, but then it vanishes.
Continuity mistake: When Elliott finds ET dressed up and wearing a wig both sides of Elliott's closet doors are open, but after ET hands Elliott the newspaper comics section ET goes over to the closet and only one side is open. Additionally, note the deliberate absence of Elliott's lounge chair which should be right beside the closet door.
Continuity mistake: After Elliott finds ET in the wig and hears him speak, when ET gives Elliott the newspaper comic section there's nothing on the yellow chair behind him, but in the next closeup a shirt suddenly hangs over the back. Additionally, the globe on the desk has turned so the continents change position.
Continuity mistake: After Elliott explains to ET how the water comes out of the bathtub faucet, when Elliott's on his knees moving closer to ET (while he's squeezing toothpaste), note there are two solid color floor mats (one white and one brownish) which disappear when Elliott rushes to answer the telephone.
Continuity mistake: In the first shot of the boys playing Dungeons and Dragons, Greg is holding the phone with the stretched out cord pulled under his left armpit, then a couple of shots later (not a continuity issue yet) the cord is pulled over Greg's right shoulder, but in the next shot it's back under his left armpit.
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 then there is a close up of her face as she gets up again.
Continuity mistake: While all the boys are trying to escape with ET, there are black brake levers/clamps on Michael's and Greg's bike handlebars, and brass brake levers/clamps on Tyler's and Steve's handlebars, but in some closeups this changes. For example, after Steve shouts, "Let's split up," Michael's are brass, when Tyler pulls off his balaclava his are black, and when Greg shouts, "Tell me when it's over," his are brass. Presumably bikes were switched for closeups.
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 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.