Other mistake: When Melina picks up Quaid on "I19", the car seat is an integral part of the door. When Quaid gets out of the car after crashing on the street, the seat is an integral part of the chassis.
Other mistake: In the chase scene on I19 Hauser pushes the throttle forward to accelerate but in the police cruiser the throttle is pulled backwards to accelerate.
Answer: The absence of the tattoo on Quaid's arm hints that the whole scenario could have been a memory, brought on by Rekall.
THGhost