When Uncle Arthur tries to get out of the second mirror (the one in the entrance), you can see that he's just offscreen to the left because his waving arm casts a shadow.
When Larry enters the house, he notices Dr. Bombay, but he says, "Who's that?" He should know him from the earlier time they worked together on the "Cold Bomb" pills.
There is no effort made to conceal the fact that it is not Uncle Arthur flying as Superman. It is so obvious a stunt double was being used.