Continuity mistake: In the exterior front shots of Elliott's house there are some significant changes to the landscape in different shots. For instance, the two lampposts at the bottom of the driveway change to an entirely different style in some shots, and the huge garden boulders repeatedly vanish and reappear. Also, note when Michael takes off on Elliott's bike to go search for ET, the in-ground lamppost that should be beside the mailbox has vanished, but it reappears when all the government agents are setting things up outside the house.
Other mistake: In all the shots of ET wearing the white sheet the two eye holes are about a foot apart, so he could see out of the holes properly, but when Michael finds the white sheet ET had been wearing he lifts the material and we see that the two eye holes are only about two inches apart, which makes no sense. (It was Gertie's sheet which had eye holes that close together).
Continuity mistake: While Elliott and ET are saying goodbye, in the original 1982 version in the shot facing Elliott, ET lifts his right hand to point his finger at Elliott's forehead and ET's finger glows (note the weird angle of ET's raised right hand), but in the next shot facing ET when he says the iconic words, "I'll be right here," it's actually ET's left hand up by Elliott's face. This was digitally corrected in the 2002 version, so that in the first shot ET lifts up his left hand.
Visible crew/equipment: When one of the government cars drives alongside the boys on their bikes as they're nearing the bottom of the hill, in the closeup of the car the reflection of a crew member wearing a cap can be seen on the back passenger window, just as the driver speaks into his radio mic and says, "We got 'em," at the start of the shot.
Continuity mistake: When Elliott's on the phone with his mother telling her even though he's sick he doesn't need a doctor, Elliott's holding the telephone receiver up to his ear with his left hand and the telephone base with his right hand, but in the next shot the two have suddenly switched hands.
Continuity mistake: While Mary is reading Peter Pan to Gertie, when Elliott shows ET the box with everything he collected from the garage, the front of the Kromedge blade faces Elliott, note the writing and the direction of the blade's teeth pointing to Elliott's right, but in the next closeup the blade faces the opposite way.
Deliberate mistake: When Elliott and ET are on the bike heading to the forest on Halloween night, ET is covered with the white sheet, but in the closeup of ET's face right before the bike flies he's covered with the white blanket (note the material), which is from the scene later in the movie.
Visible crew/equipment: When the two government agents pull over at the bottom of the hill one of the agents remains in the vehicle, and in the shot from inside the car just as Greg rides his bike over it, the crew member's (presumably cameraman) hand can be seen behind the agent's head in the rearview mirror's reflection. (It can't be the driver's hand since it gets blocked from view by the driver's head, within the reflection).
Continuity mistake: While ET is lying on the bathroom floor there's a pink and burgundy striped bath rug beside him, and in some shots the burgundy edge is beside him, but in other shots the rug is turned around and positioned the opposite way with the pink edge beside ET. Additionally, the proximity of the rug to ET keeps changing during the scene. (This rug can also be seen during an earlier scene with Elliott and ET in the bathroom).
Continuity mistake: When Elliott gets food for himself and ET he takes the milk container from the top shelf of the fridge, and we see an empty space beside the Skippy peanut butter where the milk had been, but after Elliott drops everything onto the floor, in his next two closeups note the milk container (it has a distinctive curved design) is back on the shelf in the same spot beside the Skippy jar.
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: 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.
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.
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: 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: 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)