On the Coyote's third attempt to ride the rocket, it launches completely out from under him, but when he is shown falling, the animation from the first attempt is re-used, which shows him falling with the hull of the rocket after the nosecone and fuel shot out and left him there to fall.
When the coyote first uses the "One Dozen Explosive Tennis Balls", the box has an empty spot in it -- he has taken one of the balls out to practice on a cactus. He then sees the roadrunner and takes another ball out to serve it, but when the ball is returned, it bounces past him and back into the box -- which is now full again.
The Road Runner's head changes to cyan when he runs past Wile E. Coyote towards the pipe that shrunk both of them.