When the butler falls down the stairs, he's slightly on the side, but when cut to the next scene he's on the floor face down, obvious cut from scene to scene (perhaps for changing the stunt man to the original actor).
After Horace drops the glass flower vase on the floor and it shatters, no effort is made to clean it up, nor is Morgan told to do so, yet the rest of the characters walk around as if there's no shattered glass covering the floor.
Roger and Gladys go to a barn to get liquor from the car stored there during the driving rainstorm. When they are coming back to the house, there is a large puddle of water in front of the house but no rain is falling. Roger, carrying Gladys gets almost to the door when the water is turned back on. Rain pours near the door but not on the rest of the area in front of the house.
When William is introducing himself, there's an obvious cut to the next scene; William is standing differently and he's saying the same sentence in a different way (looks like they tried to remake the blooper but kept both scenes).
Towards the end of the movie when Saul and Penderel are talking at the table, Saul uses his fingers to make the number two his palm is towards Penderel. Next shot the back of Saul's hand is towards Penderel.
The goof item below may give away important plot points.
At the end Saul sets the walls on fire, and then the two lead characters fight and fall off-screen, however all the scenes after this never show anyone trying to put out the fire but somehow the house never burns down. Who put out the fire?