Revealing mistake: There's no chimney on the roof, but the fireplace works.
Visible crew/equipment: Boom mic visible when Marcy is looking at her back in the mirror.
Visible crew/equipment: When Paul pokes the dead body with a stick, you can see a diver's arm turning the corpse over.
Other mistake: The Blazer was only hit twice by the baseball bat, once on the right front fender, and once on the grille, but it sustained a massive amount of damage. Also, when the infected guy was inside, throwing up blood, you could see that the windshield was cracked in several spots, but it was never hit.
Continuity mistake: Right at the end, when Paul checks on Karen (obvious dummy), she is lying on her right side while the dog is attacking her. After Paul gets chased out by the dog and kills it, he returns, and Karen is now on her left side. She didn't have the strength to move when the dog was biting her, so how could she turn over?
Answer: Sticking her finger up his bottom. I believe it is mentioned in one of the commentaries.