While scouting the police station, Dortmunder is approached by a mugger who takes an interest in his watch with the wide leather wrist band. The mugger is a couple of feet from him. However,when the shot cuts to Dortmunder's view of the street, we clearly see the mugger walking out of a doorway on the far side of the street.
During the initial conversation between Dortmunder and Kelp in the car, when the camera is on Dortmunder, his window is rolled up and no wind is apparent. Whenever the camera cuts to Kelp, however, Dortmunder is seen in the foreground with his hair being blown vigorously by an obviously open window.
Dortmunder is mugged for his watch, which is a wide leather banded watch whose buckle strap tapers to a thin strip. Later, in the helicopter when he says "Not me", we see him wearing a brown leather watch with a wide buckle strap this time, presumably a replacement. However, later we see him in the bar wearing a watch with a metal wristband.
When the locksmith is attempting to unlock the case in the museum, he's using only a pick. Without a tension wrench, there's no way to turn the lock cylinder, so he would never succeed in picking the lock.
The Swedish 9mm SMG used is by no means realistic. They are both mounted with the special barrel and security equipment used for firing blanks for this actual type of SMG - plastic bullets that disintegrates when fired - only used in combat training.