The reason for the rest intervals is to avoid doing any single excercise (like pull-ups) to the point of muscle failure. Instead, break up the excercise into sets of 3-5 with 3-5 minutes rest in between.
All of the serious strength trainers advocate this methodology for increasing the maximum number of reps you can do, for that given excercise. Another thing you may want to try, and this is from Jeff Martone, is everytime you walk under (or near) your pull up station, do a pull-up. Just one, everytime. You may be suprised by how many extra pull-ups you'll do in a day, how that will help increase your rep count. I just did one now.