When the guards prevent The Thief, carrying his friend on his head, from entering the gates, they completely disappear in the next shot after the gates are closed.
The bloody mark The Thief leaves on the wall disappears in the next shot.
In the final flying carpet scene, the position of the magic chest on the carpet changes between shots.
Right after the magician tests the magic apple on the man getting water from the stream, he falls down dead and his body turns black. If you look closely, you can see the "dead man's" chest rise and fall as he's still breathing.
At the 2 hour 27 minute mark when the thief and the princess are flying over Bagdad you can see piano wires holding up the flying carpet when the light reflects off them. You need to look carefully though.