The concept behind the 100/push-up/pull-up/sit up etc. is very good. I used a slightly modified version to train prior to BMT for the Air Force. Since I was entering as an "old man" (35) I figured I should go in the best shape I could to try to make the whole process a little easier.
So, as someone who has been through the challenge, I would suggest a couple of tips.
Don't be in a rush to begin with. Focus on your form... Doing such a high volume of reps, if you practice it wrong repeatedly, it will make it more difficult later on.
Breathe! So many people hold their breath. I the beginning this wont be a problem, however beyond 30 or so reps, this kills your progress. I personally prefer slow breathing,but go with what works for you. I tend to breathe in on 1,2 out on 3,4,5,6 etc. This matters a lot and would say breathing is the difference between 80 and 100.
Understand that once you can do 60 push-ups with good form, it is very little to do with muscular strengthandmuch more about muscular endurance so the goal is not be stronger, but more efficient.
@bakari, you are right it is difficult to do more than about 70 within the minute...it becomes more about "gaming" the test. I have found that by restricting my form for purposes of the test to exactly the movement required (I tend to go deeper when I train for strength) and also stopping marginally before complete lock out at the top make a big difference to the number you can crank out. A good way to practice is with a metronome. Oddly enough it is more difficult to do 60 slow push-ups timed exactly in a minute than it is 100. Doing them slowly you lose momentum.
Great to see people do this. Doing 100 consecutive push-ups with good form requires a lot of work, but it is doable! Good luck everyone! My next goal is the 50 pull ups challenge...holy smokes that one is tough!