Deliberate mistake: When Elliott and ET are on the bike heading to the forest on Halloween night, ET is covered with the white sheet, but in the closeup of ET's face right before the bike flies he's covered with the white blanket (note the material), which is from the scene later in the movie.
Deliberate mistake: At the end of the film when E.T. is leaving, there is a bright light from the ship, and wind and dust from the spaceship's liftoff. But when the spaceship has lifted off and has flown into space and made a rainbow, they show Elliot and the others and there is still the shining light, plus wind and dust blowing for no reason.
Chosen answer: They actually are smoking and there are cigarettes on the table.
Mike K