Filling holes in book shelves
Caulk would be my least preferred. (One can't sand it.) Joint compound is probably okay if you're willing to do a few coats (it'll shrink). Best would be bondo -- the car body filler. (Note that you can catch bondo at a point in its curing cycle when it's firm but pliable and easily cut flush with a sharp chisel/blade. Practice makes perfect on that one.) Texture of any filling you use versus the texture of the billy will be an issue, so you might consider rollering paint on to get an orange peel effect. I'm pretty sure Billy shelves are covered in melamine, so would strongly suggest a melamine primer. (It bonds better than normal primer.)