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.
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.
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.
Continuity mistake: When Elliott is kneeling near the bathtub explaining to ET where the faucet water comes from, there's a can of Coke beside him, and in the wideshot it's the "Coca Cola" logo facing out, but in Elliott's closeup it's the "Coke" logo facing out.
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 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 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: 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).
Continuity mistake: After ET levitates the balls of modeling clay (which Gertie had been playing with) Elliott tells Michael "something scary" is happening, and when Elliott runs toward the shed the swings on the swing set are motionless, but in the next shot one of the swings is suddenly swinging back and forth, but in the next shot it's perfectly idle once again.
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.
Continuity mistake: When Michael drives the van onto the playground and stops, in the shot from behind the three boys on their bikes Greg turns his head to look down at Harvey, who's sitting between Greg and Steve, but in the next shot facing the boys Harvey has vanished.
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: When Gertie rushes into Elliott's bedroom with the drawing she made for him, just as she sees ET and begins to scream the paper is in her left hand and her right hand is empty, but in the next shot the paper is suddenly in her right hand.
Continuity mistake: When everyone goes to the shed Michael kneels down to look closely at the prints on the ground, and in the closeup the marks we see differ from the clear prints seen in the next wideshot.
Chosen answer: They actually are smoking and there are cigarettes on the table.
Mike K