Just before Flynn cuts off Rapunzel's hair, there is a shot from behind him and he reaches up with his right hand to push her hair behind her ear. His arm is visible up to his forearm and the shackle is nowhere in sight. However, in the next, wide shot, the shackle is suddenly up around his wrist.
All of the creatures in baby Rapunzel's mobile are referenced later in the movie. The blue bird is the first creature she encounters after leaving the tower (it flies around her head when she sings "completely free"). There is also a white horse (Maximus), a chameleon (Pascal), a yellow duck (The Snuggly Duckling), and a cherub (the old man who dresses like an angel in "I've got a Dream").