Visible crew/equipment: When Dennis Weaver is in the cafe a shadow of a cameraman is cast across the table he is sitting at. The shot then changes to a wider angle to reveal that there isn't anyone near him who could have cast that shadow.
Continuity mistake: In the early scene when Harry walks across the street to confront the wounded robber on the street ("Did he fire six shots or only five?"), the shotgun used by the robber is lying several feet from the robber's hand, but when he reaches the robber, the camera shot shows the shotgun just a few inches from the robber's left hand. (00:13:00)
Plot hole: The police Inspector recounts the murders, comparing them to the ten Biblical plagues of Egypt, and he states that in keeping with this theme Dr. Kitaj was killed by rats. First, Dr Kitaj dies in a plane crash. Okay, he was attacked by rats in flight but nobody would know that - his plane crashes in a huge, violent fireball and nobody would find any rat remains after that. Second, there was no plague of rats in ancient Egypt! (Go ahead, look it up). Even if the police had made the connection between the mysterious deaths and the ancient plagues they would not make the connection here.
Continuity mistake: On Day 2, when the two officers go into the town's doctor's office, they leave the van with the driver's door way open, beyond 90 degrees, almost 180. The door didn't move to indicate it corrected itself as they went in. When they come out, the door is almost closed. And there has been no indication of a wind other than the helicopter, and that is supposed to be 1000 feet up and not even close to the office.
Audio problem: When the saxophonist talks to Eddie (Albert Finney) before joining his band, which has already started playing, the saxophone can be heard although the player has not yet joined them on stage.