After Dr. Simmons and Nurse Bethke drive away from the all-night diner, they go west. John and Mrs. Nicholson leave a few minutes later from the same location, and they are headed east, even though the destination of both parties is Santa Fe, New Mexico.
When John is talking to the CIA man on the dock at his fishing spot, the surface of the pond keeps changing between shots - from mirror-like calm to slight wind-driven waves and back again.
In the opening scene, Mrs. Nicholson's car passes the towed car, yet John Emmett's towed car gets to the garage before Ann Nicholson's Lincoln. However, it's quite obvious that John's car comes in from the left while Ann's car enters from the right, indicating that she passed the service station and then drove back. That is why John's car enters first, even thought Ann's car passed him on the highway.
When John makes the midnight stop for gas, he goes inside the diner to get donuts and coffee for Ann and himself. However, he is served his coffee in a ceramic cup at the counter, and not a to-go container as one would expect. John has decided to order a hamburger and that is later served on a plate when he is seated in a booth.
When John and Ann are in the cabin drinking coffee, their cups are empty.
There is no fishing line in the rod and reel that Sterling Hayden carries during several indoor and outdoor shots.
At the motel where Ann and John have a handyman bring them food and a hacksaw, there is no lock on the door to their room - not a chain or deadbolt or even a lock in the doorknob.
When John and Ann are talking in the car after leaving Dean Brant's place, the camera and operator can be clearly seen reflected in the car windshield.
After Ann and John are handcuffed and escape from the sheriff and deputy, John drives the car. John and Ann are handcuffed with her right wrist and his left and so he has to drive with his arm across his body with Ann as passenger. It is Ann's car and she is a capable driver so why would they travel with the awkward seating. Later, when they stop and get out of the car and then get back in John is the driver again with the crossed arms.