In the hanger when Shermin is playing the alleged Voyager golden record, the turntable is turning counter-clockwise (instead of clockwise) and is rotating at a much higher speed than the 16-2/3 RPM at which the Voyager record was intended to be played.
When Starman and Jenny are sitting in her car, looking at the map projection, it projects in the wrong direction on their faces. When the camera is behind them, Starman is sitting on the East coast side of the map. When the camera faces him, the West coast is projected on his face.
Starman and Jenny are driving in the Mustang just before the near-miss with the tractor-trailer; the sun is seen to be shining through the back window of the car, to their rear. After they pass through the intersection narrowly avoiding a collision, the sun is shining on the car from the front.
When Jenny drives on the wrong side of the road we see both vehicles spin round each other. In one shot the truck's wheels are all on the road. in the next shot the rear wheels are sliding on the grass.
When Sherman arrives at the Indian country diner the sun casts the shadows of the police cars directly towards the building. A few minutes later when Jenny & Starman leave, the shadows have moved round 90 degrees.
When Jenny and the Starman are sitting in the Mustang for the first time, she is trying to start the car. There is no key in the ignition and it is in the locked position. When the Starman starts the car a few seconds later, he touches the key which is now in the ignition, and the ignition switch is turned to the run position.
During the chase after being discovered at the hotel, the radio reports that the car was on I-80 North. I-80 is an east-west interstate as shown seconds later when they crashed through the road construction signs.
Sgt. Lemon, the crew chief on board the C&C helicopter wears the insignia of the 82nd Airborne Division on his right shoulder (indicating combat service). This has been worn with the "Airborne" tab since the end of World War I. Additionally all of the soldiers wear the "First US Army" patch on their left shoulder - the 1st US Army at the time was a headquarters unit at Fort Meade Maryland. And while it makes sense that the C&C chopper would be fitted out this way (Fort Meade is the home of the NSC) it doesn't make sense that the combat forces detailed to them in the southwest US would not be wearing their local insignia.
After Jenny fires the shots into the air at the truck stop, the gun still has the hammer forward. On the type of pistol she had, the hammer would have been cocked after firing. The same thing happens near the start of the movie, while Jenny is sitting in the box in the corner after having fainted. Starman plays with the .45 automatic, then shoots through the window glass. After the shot, the hammer is in the forward (un-cocked) position.
When the big ship is coming into the crater, Mark Shermin (Charles Martin Smith) is looking up as he stands in a group of soldiers who are looking straight out and acting like nothing is happening. Later, when the ship has come down, the scene shows Shermin looking outward and only one of the four or five soldiers is looking up with wonder.
The home movies that Jenny is watching feature semi-arid mountainous terrain, which doesn't exist in Wisconsin. But it wasn't necessarily filmed in Wisconsin. It could be video from an entirely different location.
After Starman removes the note Jenny left on the mirror in the restroom, he gets back in the car and asks her what "kidnapped" means (he pronounces it as if it has three syllables). We know he learned his limited English from the record on board the Voyager spacecraft. But he only heard the words - he doesn't know how to read them.
When Starman runs the yellow light, the loaded tractor trailer that he almost hits is approaching the intersection at highway speed, never slowing down for what would have been a red light. And considering the flat, open countryside in which the intersection is located, the truck driver, approaching a red light, would have clearly seen the orange Mustang speeding toward the intersection on the crossing road.
Sgt Lemon reports Heinmuller's near crash with the Mustang. He reports the vehicle registration number as PXV 237. There was no license plate on the front of the Mustang and Heinmuller never saw the rear plate.
The jet that shoots at the UFO was a Northrop F-20 Tigershark, a fighter prototype that never entered military service. Upon close inspection, one can see the civilian aircraft registry number on the rear of the fuselage.
The goof items below may give away important plot points.
When Jenny watches Scott reanimate the deer on the hood of the car, the "bozo" asks her if she would like some venison or a "shot of pork." The bozo sees Scott by the car and the deer has already run away - he says "that son of a bitch," and runs out the door. Jenny is seen to run after him. But in the subsequent shot, the bozo is seen running out to confront Scott, and Jenny is seen to be standing motionless at the door of the diner.
After the fight at the Bowdark truck stop, Jenny and the Starman flee the parking lot in the Mustang. They accelerate past the bus as the Chevy pursues them. The Chevy is seen pursuing them and damage is visible to the right front fender, but the Chevy doesn't collide with the bus until a few seconds later.