During the climatic fight scene, Amy's gag changes thickness between cuts.
The cut on the right side of Erin's forehead is healed after only 2-3 days, which is not possible for as deep a wound as it was when she left her husband.
You cannot purchase a car without paperwork. There is always a bill of sale or title involved.
It's not possible to talk to a police officer in another state via radio, and the device the investigator was using was not a police radio. In a situation such as the one shown, cell phones would be used.
The police car at the gas pump was a Ford Crown Victoria. It has a side fuel filler door so there would be no need for Erin to back up; it could have been filled up at the front pump where it was parked.