In two shots of Hound climbing up onto the mail plane's upper wing after The Prof rips a big hole in the wing with his grappling-hook, the hole is gone.
Tommy states that the plane he's working on "is the only one they have left", yet the next day, after his fellow pilots learn from Mrs. Hudson that Tommy's plane has been rigged with nitro and sabotaged to self-destruct, the pilots attempt to take off in other planes that are sitting around the airfield; these planes fall apart, as well, but the pilots had initially assumed that these planes were okay to fly, so it's not the case that Tommy's plane had been the only seemingly-intact one around.
Moriarty's grappling-hook is lodged in the plane's wing just in front of the spot where the bottle of nitro is attached, but then in a close-up shot of the bottle, the hook is positioned behind the bottle and is actually resting against it.
Tommy's damaged airplane is shown to be heading out towards the ocean after the mail-bag is dropped, yet the plane is then shown to be merely crossing a gap between two of the seaside bluffs.
All four tail-struts on Tommy's sabotaged biplane are seen to break loose (Hound has to hold the entire tail-section in place with his arms/legs prior to securing it with the wire), yet when he finishes with his repairs and moves forward to tie up the broken wing-braces, only one wired splice is visible on the tail-struts.
The Prof only has Smiley and Todd as helpers, so there would not be a fourth person present to impersonate the Prof --- and temporarily continue chasing Smiley who was disguised as Mrs. Hudson --- after he and Todd clobber Hound and Watson with the frying pans.
Actually Smiley was by himself, he was carrying a stick attached to a mannequin to make it look like Moriarty was chasing "Mrs Hudson".