Factual error: The government operatives go to great lengths to cordon-off and sanitize Elliott's home with extensive hazardous material preparation. Controlled airflow, Hazmat suits and everything. But as soon as E.T. "dies," everybody takes off their Hazmat masks. So, E.T. was only a Hazmat threat when he was alive? A real government Hazmat team would never drop their guard like this, as long as the alien body was still present.
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.