* Damage the paint job: The paint will be smudged, scratched, or otherwise marred by the pressure of closing the door.
* Stick the door shut: Wet paint can easily adhere to the door frame and other parts, preventing the door from opening.
Wait until the paint is completely dry and hard to the touch before even *gently* closing the door. It's best to consult the specific instructions on your paint's packaging for recommended drying times. In general, err on the side of caution and wait longer rather than shorter.