The player's head orientation (or wearable item/helmet orientation, other than the armor) seems to get stuck to the one it was at when drinking a potion of invisibility. It resets when the potion effect runs out. This can be seen by wearing a pumpkin while invisible and using F5. The head/pumpkin does not move in relation to the body while looking around. Also, the weapon and tool use/hit animations don't work while invisible. (Sword block animation does work though.)
Edit: The sword block isn't identical to normal either. The sword is in a weird downward angle.