At the beginning of the movie when Peter met Dudley, who was attempting to commit suicide, Peter pointed out that committing suicide is illegal. Assuming the movie was set in the mid sixties when it was made, this would not be true. Committing suicide was no longer illegal since an act of Parliament in 1961.
(at around 55 mins) During Dudley Moore's song "Love Me", which he sings in character as Stanley Moon, the woman to the right of the screen seems to say repeatedly "Oh, Dudley" instead of calling him by his character's name, "Stanley".
(at around 45 mins) When George and Stanley are traffic wardens, George jumps up onto the top of a red postbox which moves, revealing itself to be a prop.
Stanley is given a telescope to observe Margaret and Inspector Clarke searching for his body in a distant lake. However, he also can hear every word they say, despite having no means with which to do this.
A lot of the outside scenes clearly have been dubbed afterwards to cut down on background noise.
(at around 1h 40 mins) At the end when George Spigott leaves the Wimpy restaurant, a cameraman can be seen crouching down filming the scene, and a crowd of people watching the filming in the reflection of the glass.
(at around 8 mins) When Stanley uses a sock to plug a leaking pipe only to have it fall back out, the sock is obviously pulled out of the pipe by an off camera hand.
(at around 30 mins) When The Devil talks about The Garden of Eden being a swamp like Croydon, and then points saying it's over there, he is actually pointing roughly east towards Islington, whilst Croydon is south from their position on the tower. He could have been referring to Hackney Marshes which are in the direction he was pointing, but they were only marshes in name at the time the film was made.
(at around 3 mins) Margaret calls out restaurant orders for "French fries". In Britain, French fries are called "chips", and this is how they are listed on the Wimpy menu.
(at around 17 mins) When George files Stanley's contract, he puts "Moon, Stanley" after "Moses, Irving".
George's surname above his shop is Spiggott. In the end credits, it is Spiggot.
The Devil, who should know these things, doesn't know that a Dutchman, Hans Lipperhsey, invented the telescope, not Galileo. However, Lippershey's patent application was rejected, and Galileo, having heard of the invention, promptly built his own better telescope, which he made his observations with.