The chest piece on the suit of armor alternates between dented and undented.
When Shemp hits the wall and loosens the shield from above him, it can be seen that it's a curved shield, but what hits him on the head is a flat one.
When Shemp offers the ghost in the armor "a smoke", the specter says he hasn't had a smoke "in a thousand years". Even though the spirit is from the time of Lady Godiva (11th century), smoking did not come to Europe until the 17th century. So the longest that the spirit would have done without a smoke was about 300 years.
Visible strings (or wires) abound; the armor's visor, Larry's hat, the frog, and the skeleton. (To be fair, this is a by-product of digital restoration, which results in a much sharper and clearer image; the wires were not visible in its original theatrical release.)
The tailor opens a window to be able to thread the needle. He then hears cheers and yells and looks to see what it is about. However, he said all the shutters in the city were shut, so no other person would have been looking to see Lady Godiva. Therefore, no cheering and yelling would have happened.
Lady Godiva (well the spirit of) wears a dark swimsuit. The legend of Lady Godiva has her riding through the town naked.