Revealing mistake: During the scene in the woods with the communication machine, Elliot tells E.T. that they need to go. You see the machine still working at a regular interval because a rope is pulling it. The shot pans to the left a touch and the rope stops moving, as if the person pulling it realises it's no longer in the shot.
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: When the boys are riding their bikes trying to escape with ET, all the bikes have single brake levers on the right side of their handlebars, but after Elliott shouts that they should follow him to the forest, there's a shot from the POV of one of the bike riders (we know it's not Greg or Elliott) and he has two brake levers on his handlebar.
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.
Other mistake: When ET launches all the bicycles into the air, first there's a closeup of Michael, then in the next closeup of Steve as they climb higher he leans back with his arms outstretched, as if he's balancing himself on his bike, and we see Steve's right hand making a fist pretending to grip his handlebar, though he's not actually gripping anything at all, it's an empty fist. (This shot has nothing to do with CGI disappearing issues).
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: 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.
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.
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).
Visible crew/equipment: Near the start, while the agents are chasing ET, after the last closeup of the jangling keys it cuts to a shot of ET moving fast through the forest and the equipment used to help him move can be seen. This is only visible in the original 1982 unaltered version (such as on Netflix), because ET has been digitally altered in the 2002 version. Interesting to point out that the 2002 2-disc DVD set, which includes the 1982 version, has also been digitally altered in this shot.
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: After ET weighs himself on the scale there's nothing draped over the side of the bathtub, but in the next shot we see in the reflection that there's a burgundy tub mat hanging over the side of the bathtub, behind ET and Elliott. Then that tub mat vanishes again when Elliott rushes to answer the telephone.
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: When ET is trying to tell Elliott and Gertie that he wants to phone home there's a chip bag on the table in front of the turntable, but it disappears when Michael comes home and ET points out the window and says, "ET phone home," then the chip bag reappears when ET pulls off the wig.
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. The mistake occurs in a long shot, when the boys start riding behind the first house under construction, and are followed closely by the blue station wagon. (01:41:15)
Continuity mistake: When Elliott's holding the Kromedge saw blade in his hands, note the position of the writing on the blade and the position of his fingers within the blade's teeth, then after he slices the index finger of his left hand there's a closeup of the blade with Elliott's blood on one of the teeth. The problem is that Elliott's index finger was actually on the blade tooth further along the blade's circumference (note the writing).