When do I need to take down the mobile hanging over my child's crib?

Mobile movement. A good time to take a mobile down is when you transfer your child to a regular sized bed from a crib. That way he won't be reaching for it and possibly fall out of bed and injure himself.
When baby grabs it. When junior is tall enough to grab it, down it will come. You can remove it entirely, or hang it from a higher loop from the ceiling, well out of reach.