Continuity mistake: When Keys turns around to see what's rustling in the bushes behind him, his flashlight swaps hands between frames. (00:05:50)
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: When Elliott asks Mike about joining the Dungeons and Dragons game, Steve turns his head toward Elliott. In the next shot Steve is staring down at the kitchen table instead. (00:08:45)
Continuity mistake: As Elliott creeps up to the tool shed with a pizza box, watch how the porch swing rotates 180° from one shot to the next. (00:10:15)
Continuity mistake: After being discovered by Elliott in a cornfield, E.T. panics and escapes through the back gate, which closes by itself. But in a following shot, the gate closes again. (00:14:45)
Continuity mistake: When Mike suggests that Elliott saw an iguana instead of an alien, Mary holds a coffee mug halfway between her mouth and the tabletop. Between frames the mug changes position and is now within a couple inches of her mouth. (00:17:05)
Continuity mistake: When Mike rolls Mary's Audi into the street, his head goes from being within the vehicle to poking out between shots. (00:26:30)
Continuity mistake: In the scene where Elliott is talking to E.T. for the first time, a shark pincher can be seen hanging over the fishbowl in the foreground. But as he starts pronouncing his name ("Ell-i-ott"), the pincher briefly vanishes. (00:28:00)
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)
Continuity mistake: As Gertie lifts a flower pot and places it in the wagon, the overhanging green leaves near her left hand disappear as the shots change. (00:37:15)
Other mistake: When ET walks to the fridge, there's a shot of Elliott's classroom with the camera moving towards him. Watch the chubby kid on the right, who can't help staring at the camera for a brief second. (00:44:15)
Continuity mistake: After Elliott burps during class, notice the blonde girl in blue. Her arms are crossed differently depending on the shot. (00:45:10)
Audio problem: When E.T. is home alone using the Speak & Spell for the first time, he types in E at one point, but the electronic voice can be heard saying F instead. (00:46:10)
Continuity mistake: After E.T. clicks the TV set on, the way he holds the remote control differs between cuts. (00:46:20)
Continuity mistake: When E.T. is in the kitchen reading comics, he glances over at the TV then takes a look at the coffee table which has, among other items scattered on top, six pack rings. A few shots later E.T. is at the coffee table working to create a communication device, but now there's one can of beer attached to the rings. (00:48:05)
Continuity mistake: After the frog incident, Elliott opens Gertie's closet doors to reveal E.T. dressed in drag. He initially grabs both knobs and starts pulling, but in the following shot no hands are seen gripping the knobs and the doors open up automatically. (00:53:40)
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)
Revealing mistake: On Halloween when the kids are getting ready to go trick-or-treating, Mary tells them to return one hour after sundown. But as E.T. turns around to look at her, human legs are visible below his ghost outfit. (01:02:30)
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 Mary gets her first look at an ailing E.T. lying on the bathroom floor, she panics then hurries everyone downstairs - leaving E.T. behind. Moments later one of the astronauts happens upon E.T. and now a bright pink bath towel can be seen draped over the bathtub's edge, which wasn't even there to begin with. (01:16:00 - 01:17:55)
Chosen answer: They actually are smoking and there are cigarettes on the table.
Mike K