I don't see anything wrong with the program, and pushups are fine, but are not a complete workout. I'm sure it would be fun to have a goal of being able to do 100 pushups, and the plan seems to be easy to follow and motivating.

If I were going to do a plan like this, I'd do burpees, instead. Burpees use a lot more muscle groups, and are going to help the cardiovascular system more than just pushups. It takes A LOT longer to get to 100, though...

Edit to add a video that shows how to do burpees:
http://www.youtube.com/watch?v=c_Dq_NCzj8M