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.
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. (01:51:20)
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: 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.
Continuity mistake: When Elliot is leading E.T. up to his bedroom for the first time first his shadow is in front of him on the candy, then in a reverse shot it is behind him.
Visible crew/equipment: After Mary and all the boys look in the shed and find tracks, when they head back to the house Tyler stops at the pizza box, and note the three distinct marks on the ground to inconspicuously signify where actors should stand while discussing the pizza. Michael stands at his curved mark, Elliott stands at his L-shape mark, and Mary's mark is in the shape of a T-mark.
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.
Continuity mistake: After Mary carries Elliott downstairs the government agents start entering her home, and in the next closeup of ET lying on the floor there's a large bath towel hanging over the side of the bathtub, but in the next shot of ET from behind the "spacesuit", there's now a small bath mat (same color as the previous towel) hanging over the side of the tub.
Continuity mistake: When Mary and the boys go to the tool shed after Elliott's encounter, as Tyler and Michael kneel down to inspect the tracks on the ground, the trash can beside Tyler is partially under the table and a roll of fencing is upright behind him. However, after Michael mentions the coyote, the trash can is now to the left of the table, the roll of fencing is lying on the ground in front of the trash can, and some long-handled tools have moved as well.
Continuity mistake: When Elliott is trying to lure ET into his room by leaving Reese's Pieces on the carpet, the red helmet is lying on the table with its white stripe facing the doorway and its opening facing the bunk-bed, but when ET reaches the doorway the helmet has turned itself around so it's facing the opposite way.
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. (00:08:45)
Continuity mistake: After Mike finds E.T. lying in a river, the scene switches over to an FBI agent's shadow cast upon the driveway at Elliott's house. Notice how the front doors are bare. Minutes later when Mike opens one of the doors to see an astronaut waiting outside, large Halloween decorations are now tacked upon it. (01:15:20)
Continuity mistake: When the two government agents pull over at the bottom of the hill to cut the boys off, in the shot from inside the car we see Greg and Tyler riding their bikes over the car and zooming off, then the agent inside the car lifts his head as yet another bike lands on the car, but in the next exterior shot it's Tyler (note his black high-tops) who lands on the car's roof, knocking off the magnetic beacon light. (Elliott's conspicuously missing from these few shots).
Continuity mistake: In the scene where Elliott and E.T. are behind the slatted closet doors listening to Mary read Gertie a bedtime story, the set of slats nearest the door frame opens by itself between shots (right about the point where Elliott wraps a scarf around E.T.'s neck). (00:59:00)
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. (00:37:00)