Using "Pop" Rivets
  "Pop" rivets is actually a name brand, and they are more correctly called blind rivets.

There are many advantages to using blind rivets, and a few disadvantages.  Chris Heintz has written a couple of articles going over their proper use, and are linked here:

Chris Heintz's articles on Rivets - Part 1

Chris Heintz's articles on Rivets - Part 2

One disadvantage I've heard several times is that the steel center of the blind rivet can cause problems, rusting out and causing the paint to come off after some time.  Below are photos I took of a 1970 Pazmany PL-4 that is all blind rivet construction. After carefully looking over the surfaces, I found no evidence of any corrosion coming from the rivets after 30 years of flying.
   

Images on this website are either Copyright Zenith Aircraft Company and used by permission or are copyright Gary Liming