Continuity mistake: When the old car blows up both of the dead zombies are gone. (00:21:40)
Continuity mistake: When a zombie's head is held up in the truck to be shot, there is a big splatter of blood down on the face of the soldier. He wipes a very small amount of blood off, but when he gets into the other truck he is perfectly clean. (01:05:05)
Visible crew/equipment: When Roger hits the zombie with the truck, notice at the bottom right a trampoline from which the zombie jumps off. (01:04:55)
Visible crew/equipment: After the main characters have entered the mall through the skylight, and have gone down the stairway in order to secure the mall, Scott Reiniger and Ken Foree open the door into the corridor leading to the control room and boiler room. Whilst walking through said doorway, there is movement in the shadows in the top left. This has to be a crew member, as the only other zombie that is in this area is in the boiler room.
Continuity mistake: When Roger and Peter are blocking the entrances with the trucks, Roger kills a zombie with a long beard that is walking towards him between the trucks. Later on in the movie, we see the same zombie, in the same clothes, outside the doors, trying to get in. (01:07:35 - 01:17:15)
Continuity mistake: When the sweater vest zombie first goes up to the 2nd floor he appeared coming up to the 2nd floor moments later.
Continuity mistake: Peter and Roger are attempting to hold off some approaching zombies while trying to get the door to Penny's shut. Peter then throws his gun and the keys into the store. In the very next shot he is trying to pull the same keys out of the lock on the door. (00:37:35)
Other mistake: In the aerial shots of the semis being driven in the mall parking lot, the zombies are milling about. Notice they have left a path just clear enough for the truck. (01:02:40)
Visible crew/equipment: When the two kids in the airport attack Peter and try to bite him, notice in the top right corner a crewmember's hand comes into shot. (00:25:40)
Factual error: When they are refuelling the helicopter (as a zombie approaches quietly from behind) the actor has put the gas nozzle not into the hole for the gas tank, but into one of the foot-holes that helicopter mechanics use to climb up to the top of the helicopter to do repairs. It doesn't even fit properly. (00:22:55)
Revealing mistake: The female zombie grabs onto the back of the car and is dragged through the mall. Stephen shoots the zombie in the eye and if you look closely you can easily see this is no longer the woman from before, but actually a man who doesn't resemble her at all.
Revealing mistake: When the bikers are grabbing their weapons, we see a grenade. You can tell that it is fake because the bottom is bored out.
Continuity mistake: In the beginning of the movie at the TV studio, Steven tells Fran that they are meeting at 9:00 to take a helicopter out of town. When they take off in the helicopter and fly away, there is a giant digital clock on a building in the background that reads 6:00. (00:05:05 - 00:18:50)
Continuity mistake: When the bikers are in the mall, a zombie is killed next to a teepee. Another zombie is pushed into the teepee knocking it over. As it falls, you can see the first zombie starting to roll out of the way. (01:47:45)
Continuity mistake: When Stephen shoots a zombie clinging onto the car, whilst driving off there manages to be a streak of blood in front of the zombie where the previous take took place. (01:17:10)
Continuity mistake: After parking the first truck in front of the mall doors, Roger jumps out and runs towards Peter's truck. Notice the zombie wearing the red and black striped rugby shirt. After Roger runs past him, he breaks zombie character and becomes concerned about his shirt being tucked in. (01:00:50)
Visible crew/equipment: When Peter and Stephen are locking the glass doors to the mall, you can see reflections of the cameraman in the glass. (01:17:45)
Visible crew/equipment: When Peter is shooting through the door a hand can be seen in a few frames.
Revealing mistake: When Peter (and Stephen) are locking all the doors, Roger gets his rifle from the back of the car and shoots a zombie. Even though the bullet goes into the side (two-inches away from the middle of the zombie's head) a small amount of blood shoots out the middle, and something at the edge breaks off/moves, revealing that it's a tomato sauce sachet stuck to the actor's head.
Continuity mistake: At the TV station, when Fran takes control of the camera, notice a man with a sweater and a beard behind her, but in the very next scene the same man appears with a different shirt on. (00:04:40)
Answer: One of the cops that was with Joe Plato (how much you have seen of them will depend on which version of the movie you, but I HIGHLY recommend the fan made/edited 'Extended Mall Hours' cut on YouTube) asked them for cigarettes. You'll notice that Roger and Fran lit up cigarettes as they were taking off, that's what Roger was laughing at.