Hot asphalt does not harden as soon as it comes out of a dump truck. The firefighters would have only needed to shovel it away from the car.
The lady had wax all over her face when she was found. It would have taken the emergency crew some time to arrive. When they get there they cut the wax covering her mouth so she can breathe and claim that there was wax in her throat. If the wax was preventing her from breathing she would have suffocated by the time the emergency crew arrived.
When Buck sits down to have his blood drawn, the cable of his mic attached to his chest is clearly visible under his T-shirt.
After Buck get's confronted by his ex-roommate and his wife the firefighters rush out on a call but in the background a guy who is clearly part of the set crew walks between the ambulances, see's his mistake and steps back.