Do puffin beaks have vertical slits or cracks?
No, as far as I am concerned a healthy puffin hasn't got any slits or cracks in its beak. The lines that you see are literally just that - or little grooves. Obviously, beaks might show signs of wear and tear, so cracks may be observed. However, there are no genes in a puffin's genome that would lead to the expression of slits and cracks in its beak.

I think the photos below might help visualising.


(Photo: Tycho Anker-Nilssen, NINA)


(Photo: Will Nicholls)