Revealing mistake: When the second piece of scenery falls on Frank, it has a tear halfway down and a hole in it that Frank's head goes through. A few seconds earlier, these weren't there. Maybe they were put there to make sure Frank's head went through, or else this is the second take.
Visible crew/equipment: When Frank is loading the lorry at the warehouse, he drives the forklift onto the lorry, then the lorry drives off while he and the forklift truck are still on the back. As the lorry pulls away you can see the camera crew on the other side of the road filming the next shot.
Continuity mistake: When Frank is demonstrating his star trap to Father O'Hara, Frank comes up through the stage floor too fast and grabs hold off a length of material stretched across the top of the stage which falls down onto the stage floor when Frank falls, but in the following shots of the scenery collapsing this piece of material has disappeared.
Continuity mistake: Mr. Finney is explaining the mirror signal manouver procedure to Frank during his driving lesson in the white Mini. While they are parked, the shots from inside the car show a line of parked cars behind the white Mini. But when Frank moves off, the shots from outside the car show no cars parked behind the Mini.