Hmm. The odometer is gear driven and so if it is working then we know the cable is turning and that tells us the transmission gear is probably ok. The speedometer needle relies on magnetism to make it spin, but if the needle jumps a bit when the rear bit is spun by hand that implies you do have magnetism. Make certain the needle isn't binding on the speedometer glass or somewhere on the dial. It won't take much to disable it even though the magnetic part is spinning...
