Other mistake: When Paul Blart is pwning Rock Band, the vocals shows the tambourine/clap notes. Paul Blart is doing nothing that would play those notes (singing or pressing the "a" button).
Other mistake: When Paul is putting on the Hello Kitty bandaid, you can see the outline on his skin from another bandaid, from previous takes of this scene.
Other mistake: The glass in elevators is tempered. It would not have shattered when the robbers pursuing Paul crashed into it.
Other mistake: When Blart and the SWAT guy are pursuing the bad guy, they have a blue police light on top of the car (the magnetic kind). Interior views of the car show blue flashes on their faces, which is impossible with the light being on the roof. The exterior shots confirm that the inside of the car is completely dark. (01:21:30)
Other mistake: In the beginning of the movie, Paul is at the NJ State Police training grounds. The training grounds, while near the ocean, do not have any islands just off the coast, nor is the ocean water nearby. The police cars used are painted light/metallic gray Massachusetts State Police colors with a blue stripe down the side. NJ State Police cars are white with red or red/blue lightbars with a blue & gold triangle logo on the front doors.
Other mistake: It is November, since Blart is worried about Black Friday. The kid's clothing store they are seen walking by toward the beginning of the film has Summer clothing and bathing suits in the window. I used to to work in retail and while stores were far ahead of the weather, they are never that far ahead.
Answer: Paul explains to Pahud that it's a misunderstanding, and Pahud then makes Paul Blart his homie.