Continuity mistake: During the song 'Thomas O'Malley', Thomas jumps on the tree and shakes one of the branches to make the petals fall on top of Duchess. Just before they hit the ground, a whole bunch of petals appear on the ground out of no where and some of the petals that were falling to the ground disappear once they hit the ground.
Continuity mistake: There is a name plate above the cat door that appears and disappears.
Deliberate mistake: I know this has been disregarded for the fun effect, but gasoline motors require air to work. When Edgar drives his tricycle into the river while being chased by Napoleon and Lafayette, it should have stalled and stopped working.
Continuity mistake: When the horse bites Edgar's coat-tails at the end of the film, in the next shot his coat is whole again - same error as when the dogs bite his pants.
Continuity mistake: When the cats are on the piano during the "Everybody Wants To Be A Cat" sequence, there is a sheet of music in front of the pianist. When we see the piano and the cats falling through the floors, the music sheet has gone.