Walls and Ceilings - Painting new drywall

Can I go ahead and paint even if the corners are just a little dark (not dry), like only half an inch wide?

I am assuming you are refering to the joint compound not being completely dry. NO, you need to wait until the corners are dry to prevent future peeling. The problem with painting over damp mud is that the paint will dry before the mud, therfor not adhering to the mud. I would also suggest useing a drywall primer prior to painting, especially if it is a type of gloss paint you will be topcoating with (eggshell, satin, semigloss)

Chip - Painting forum moderator