Plot hole: With people around the world turned into zombies, there is no way to maintain power plants, thus no lights should be lit, not to mention the functionality of an amusement park.
Suggested correction: The sequel film gives this a (very flimsy) justification, saying that everything runs on power from dams. Stupid, but at least trying to explain things.
Continuity mistake: When Wichita and Little Rock are about to enter Pacific play land. you are able to see Wichita wearing the hair loose. just after crossing the main door, Wichita is wearing her hair tied.
Suggested correction: Her hair is always tied.
Character mistake: When Tallahassee firsts meets Bill Murray, He says "six people left in the world and you're one of them." At that point they only know of 5 - the 4 main characters and Bill Murray.
Suggested correction: His character thinks there was another woman that Columbus hooked up with in the back of a FedEx truck.
Visible crew/equipment: Just before Tallahassee tears up the minivan, a crew member's legs are visible below the posters in the window of the Citizens United storefront. (00:36:00)
Suggested correction: It's the legs of Tallahassee himself in the reflection, and they copy all his movements exactly.
Revealing mistake: During the opening scenes, just before the "double tap rule" a car hits a zombie in a security guard uniform. The windshield breaks a split second before the zombie hits it.
Suggested correction: The glass breaks at absolutely the right moment just when the zombie hits it.
Visible crew/equipment: The scene where Tallahassee is smashing the windows of a black parked van in anger, note a cameraman's legs come into shot below a poster in the shop window directly in front of the van.
Suggested correction: It's Tallahassee's legs! Extremely obvious in a window reflection.
Other mistake: After Columbus wakes up and realises the girl he let stay the night has turned into a zombie, he repeatedly hits her over the head with the commode top, but in the next shot, it is clean as a whistle - there is no blood or head matter on it at all. Also the bottom of the lid is real with grooves and crevices but after the second hit in the living room the bottom ridges are perfectly oval and smooth.
Suggested correction: He hit her in the place where there is hair on the head, he left no wound there, why in the world should be marks on the lid? It would be a mistake if there were marks after the impact shown.