Other mistake: At the very end, a plane just sitting at the gate was used to simulate one preparing to leave. The landing gear ground safety pins (with red streamers) were still installed as the engines were started, but the pins have to be removed beforehand to keep personnel clear when the engines are running.
Continuity mistake: After the bank robbery, Bill Murry is robbed, and the robber takes his wallet, which contains 4 one dollar bills. As the robber walks away, we get a glimpse of Bill's shirt, which is not tucked in and we can see money strapped to his body. But a bit later, we again see Bill's shirt, and this time his shirt is tucked in back and front - there is no money to be seen, and Bill never tucked his shirt in.
Visible crew/equipment: In the very beginning of the movie during the opening credits, we are shown a picture of a park and then the camera zooms out and slides down a row of subway passengers, ending on Bill Murray. During this scene, you can see the reflection of the camera crew as it moves down the line from passenger to passenger in the windows of the subway train.