When standing in front of the facility and being attacked by Z's, Doc's standing before the van. The van's door behind him is clearly open. However, when he turns to get into the car, he has to open the door first.
When Doc finds the cell phone that is charging, The iPhone appears to be only half charged as opposed to 100%. The phone is clearly being actively charging and having been plugged in for 3+ years, it should be done charging.
In the van 10K says he has 6,998 zombies to fill (to make 10,000, the source of his nickname). That puts his total at 3,002. After his first kill in the facility he declares that kill to be number 3,002. He's off by one somewhere.