How did the Gov find Andrea in the first place? She's running cross country through a random field. Sure he knew her general direction, but it really shouldn't have been that easy. The same goes for finding her again in the building and again outside the prison. He's got to be a world-class tracker.
I yelled at my TV (probably like most) that Andrea should've taken his truck! She didn't even bother to check for keys. Hot wiring is more complicated than she could handle, but disabling?? In TWD world, simply yanking an ignition fuse or pulling a sparkplug wire would be enough to ensure if he survived he wouldn't be able to follow her by driving.