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Revealing mistakes
When the boys are racing away on their bicycles from the Feds, the stunt doubles for Elliott and his friends are obviously way too tall to be children.
E.T. is shown to be fairly large (he and Elliott are actually about the same height, since at the end of the movie, E.T. gives Elliot a hug without Elliot's having to bend over much), so there is no way that he could have fit his bulky form into the BMX-style bike's front basket; he would also have been much too heavy for the young slight-figured Elliot to be able to pedal and balance the bike with E.T.'s weight at the front of the bike.
In the 20th Aniversary Edition, when Elliott is showing E.T. the bathroom and is then on the phone with his mother, the Coke can changes designs. At first, it is the older version from 1982, then it changes to the updated 2002 can design. It switches back and forth for the entire length of the scene.
The size of the eye holes on E.T's ghost outfit change shape and size several times (most noticeable when Michael finds the abandoned outfit when he is looking for E.T.)
Gertie's hamburger changes size and eventually disappears (inconsistent with her eating it).
In the shot of the spaceship taking off at the end, all of the people surrounding it on the ground have disappeared.
In addition to the other lunar errors, at first we see a
crescent moon then the famous full moon being crossed by the bicycles (later to become Amblin Entertainment's signature logo). From thin crescent to full moon takes about half a lunar cycle, 14 days, but the time frame of the movie suggested only a few days at most.
When Elliott goes to sleep outside to look for E.T., the moon is directly behind him. When he is awakened several hours later, the moon is in the same position.
The movie is set in California and there are several police cars when the government comes to the house and pursues the kids to catch E.T. The front of the police cars are missing a steady red light. Even during the time the movie was made, in California, all police and emergency vehicles in California require at least one steady red light facing forward.
The kids on the school bus would not be allowed out of their seats throwing paper wads at each other.
Some are confused when E.T. magically heals Elliott's cut finger that the blood disappears. E.T.'s true powers are not fully known so it is possible E.T. made the blood go back into his body along with healing the wound.
When "Keys" goes inside the Clean room created for E.T. and Elliott, he and others wear a "Clean Suit", but the tubes coming out of the helmet go nowhere, not even a filter, meaning they are breathing contaminated air and that the suit is useless.
When the boys are racing away on their bicycles from the Feds, the stunt doubles for Elliott and his friends are obviously way too tall to be children.
One of the boys moves his lips in sync with Elliott's line, "Nobody go out there."
[20th Anniversary Edition] The government agents and police have had their hand guns replaced with walkie-talkies, but they are still extending their trigger fingers for no apparent reason.
[20th Anniversary edition] When E.T. is eating potato salad and drinking beer in front of the refrigerator during the scene when he is alone at home, the shadow of his head cast on the fridge door is that of the original puppet, not the CGI head.
Near the beginning of the film, when the trucks race through the woods approaching the expected location of the spaceship landing, one of the trucks "screeches" when it stops. A vehicle's tires would not screech on wet, muddy ground.
When Mary reads "Peter Pan" to Gertie, there's a view of her silhouette on the closet door slats. Her lips don't match the narration.
When E.T. takes a can of beer from the fridge, we see Harvey the dog bark twice - but we don't hear the first bark.
When E.T. is typing on the toy, he presses the "E" button when we hear the toy say "F" in the spelling "S-W-V-U-A-F-P".
When Elliott, Michael, and E.T. arrive at the park after escaping the scientists, a ramp can be seen where they drive over the curb.
As Michael leads Mary into the bathroom where Elliott and E.T. lay sick, the camera dollies backwards, brushing past and visibly disturbing an indoor bamboo tree.
The silhouette of the stuntman wearing the E.T. gloves can be seen through the railing when Elliott is luring E.T. with the Reese's Pieces.
Right before E.T. reads the Buck Rogers comic he yawns and rubs his head. While he is doing this, you can just barely see the crew moving in the corner of the oven reflection.
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.
Almost everything about the phases and appearance of the moon is wrong for the northern hemisphere.
E.T. twice demonstrates his ability to lift himself into the air using his telekinetic abilities, notably towards the end when he helps Elliott, Michael, and his friends escape the authorities. He could have just used these powers to return to his spaceship before it escapes at the beginning of the film.
Elliott and Michael dress E.T. as a ghost on Halloween to make their mother think it's Gertie. Because E.T. appears much shorter than Elliott and Michael compared to Gertie, it should have been obvious it wasn't her.
Seeing as Elliott's house was blocked off by police while under quarantine, Elliott and Michael should not have been able to steal the van and drive off with E.T.
After E.T. has apparently died, one of the medical staff is dictating a report and says; "Cardiac arrest was terminated at 1500 hours and 36 minutes". "Cardiac arrest" is a way of saying that the heart has stopped, so it makes no sense to stay that cardiac arrest had been terminated. The line should have been either; "Cardiac arrest occurred at 1500 hours and 36 minutes" or "Cardiac activity terminated at 1500 hours and 36 minutes".
Elliott's friend Greg asks him why E.T. can't "just beam up", like they do in Star Trek. Elliott replies that "this is reality" and, thus, such actions are impossible. But Elliott and his siblings had previously witnessed E.T. use his telekinesis capabilities to make objects rise, float, and move around in the air. Plus of course, Elliott himself had been made weightless and flown through the air while he and E.T. were on his bike on Halloween night, and so Elliott should have realized that "reality" as he knew it was not the same in E.T.'s presence --- since E.T. could, indeed, make even moderately-heavy objects levitate at will, it was very probable that E.T.'s fellow scientist-beings had the same powers with which to lift and transfer one of their fellow brethren onto their spaceship, and perhaps they had also equipped their spaceship with tractor-beam capability.