Continuity mistake: When Fletch and Stanwyk first meet and Stanwyk asks Fletch to come to his home and hear his proposal, Stanwyk is wearing a suit/tie on top but is wearing jeans on the bottom. In the next wide shot as they leave the beach, and again in the next scene as they arrive at Stanwyk's house, he is wearing suit pants.
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.