So far, a tamed donkey and wolf have gotten stuck and cannot be moved. The donkey got stuck on a block of dirt and the wolf got stuck on a block of sand. The donkey could be mounted, but not moved. The blocks of dirt underneath were destroyed to see if it would dislodge the animal with no success. The tamed wolf was on a lead and the lead would extend past its normal programed length in response to the animal being glitchy... both events happened on separate games and in different circumstances.