Continuity mistake: The note Jenny puts up in the restroom changes; when Starman goes into the bathroom while Jenny is signing the receipt, notice that the postage stamps holding the note to the mirror are now in different positions and the word "help" is smaller. (00:35:55 - 00:36:45)
Factual error: When Jenny Hayden and Starman accidentally overshoot their destination and arrive in Las Vegas, Jenny discovers that her wallet is missing. She has no cash, no credit cards, and no identification whatsoever. The only money she has is a single quarter. Starman uses the quarter to hit the jackpot on a 25-cent slot machine, then uses the prize money to play the Horseshoe $500,000 slot machine, which he also wins. They then use the giant jackpot money to purchase a brand new Cadillac and drive it off the lot. Huge problem: In 1984 (and today), you could never collect a giant Las Vegas jackpot without several pieces of personal identification, for tax purposes. Likewise, you could never purchase and drive a brand new Cadillac off the lot without multiple pieces of identification and a financial disclosure statement (if paying cash).
Factual error: When the government agents are reviewing the trajectory of the spaceship, the map is oriented incorrectly. Instead of Winslow, Arizona, the plotted trajectory is actually somewhere in north east Pennsylvania.
Suggested correction: The map is correct. We are looking at it upside down (from the camera's perspective), and the dashed purple line terminates about where the crater is in Arizona, and the red line terminates in Wisconsin. No line passes over Pennsylvania. It does bring up the issue though that the shoot down engagement happened over Canada, near Moosonee, so why are US Air Force F-4 jets in mid/northern Canada firing missiles?
Continuity mistake: The weather changes at least twice during the end sequence at Meteor Crater. Take a look at the clouds in the background of all of the shots, especially those looking at the San Francisco Peaks (near Flagstaff, AZ). The extreme long shots of the helicopters coming show dark clouds, while the wide shots show a mix of cloud free and then cloudy skies.