When Rupert is talking to Brandon and holding two plates of ice cream, the camera moves behind Brandon's back to make a cut. When the camera re-emerges, Rupert and Brandon are standing in the same positions, but the doorway background is in a different place. Also, the ice cream topping has changed from chocolate to caramel. Furthermore, the piece of cake changes position on the plate in Rupert's left hand - it moves to the opposite side.
When Rupert describes how he would "get rid" of David, the camera pans from the easy chair to the piano. When it returns to the chair about ten seconds later, the chair is facing a different direction.
During the tussle between Philip and Rupert, the gun fires and injures Rupert's hand. Following which Rupert takes his handkerchief to tie his wound. But he only manages to loosely hold it in his left arm. Then, when he walks over to the chest and opens it, shot the handkerchief is perfectly wrapped around Rupert's wounded arm.
During the opening credits - and judging by the windows on the opposite side of the street - the camera appears to be positioned roughly at the third, possibly fourth floor height at the most. However, the window view throughout the film suggests a flat on a much higher floor.
As Brandon and Philip walk back to the kitchen after finding the rope, the frame over the doorway into the hall can be seen separating. Since each reel was filmed in one continuous take, sets had to be moved out of the way during the shot, allowing the camera to follow the actors between rooms. (A similar mistake is visible in the tracking shot out of Bob Rusk's house in Frenzy.)
The goof item below may give away important plot points.
Incorrectly regarded as goofs
Some viewers have noted that the police are summoned after three shots are fired out the window whereas nobody seems to notice when one shot is fired in the apartment during the scuffle for the gun.
A single shot muffled by the apartment walls would not attract nearly as much attention as three shots fired out an open window.