Should I fill in 15-20 nail holes in my roof underlayment? If so, how?
Yes, I would repair it with the same, or similar underlayment if I could. I would create small round patches, about 4 - 5  inches in diameter and then glue them down with a caulk that can stand up to those temperatures. Most roofing caulks would work well. Just be sure to make the job as smooth as possible; wipe away any excess caulk.