Continuity mistake: When Shifu is speaking to Oogway under the mystic peach tree, he slams the ground, causing a large number of peaches to fall. In the following wide shot, only a few peaches are on the ground - none of which are even close to Shifu, who hasn't moved very far from his original position.
Continuity mistake: When Tai Lung is at prison, and he breaks his shield-thing off, the guardians fire four arrows at him and he evades all of them. He uses the fourth and last one to break the shackle off his hand. But in the next camera angle, there are five arrows stuck in the floor. Where did the fifth one come from?