Continuity mistake: During the scene where Fletch is at the hospital trying to locate Stanwyk's medical records, he drops lots of files on the floor and asks a nurse to sort them out. When he is talking to her he has a stethoscope in his ears, but when the camera moves behind him they are suddenly round his neck. Moments later they are back in his ears.
Continuity mistake: In the scene where Fletch is in the chief's office, he get thrown up against the wall of pictures. There are two pictures over his left shoulder and the top picture drops to the floor. After cutting to the chief and then back to Fletch, the picture is back on the wall making it two over Fletch's left shoulder.