Factual error: During the orphans' rendition of "You're Never Fully Dressed Without a Smile" Molly is seen with a plastic drink bottle (that makes a plastic-bottle-esque "thunk" when thrown). The movie takes place in 1933, however polyethylene terephthalate (the kind of plastic used for drink bottles) was not developed until 1941.
Factual error: Unbelievable that for 30 years no one has pointed out that in every shot with the moon, except when the moon is full, the crescent is pointing the wrong direction. In the evening (ordering pizza), in the Northern Hemisphere (California), a crescent moon will always be pointing down to your right (the bright side will be on the lower right). The only time it could point the way it does in these scenes is in the wee hours of the morning, at 4 or 5 a.m. and looking to the East. Spielberg didn't even fix it in the re-release.
Suggested correction: Actually the problem with moon scenes that we see a crescending moonphase (less than a quarter) when Elliott first meet E.T. After that in a couple of days there is a full moon which could be reached in about 16-17 days from that phase which we saw first. It would be also about 11 days if the first shot was mirrored and actually was an increasing moonphase. But the whole story is about 6 days long. So a full moon couldn't be reached from a quarter of moon.