It's as safe as exercise ever is. You can still pull muscles. You can still tear tendons. Both of these are generally more likely to happen if you're not paying attention to your body or trying to rush through. Bodyweight exercises tend to be a bit safer overall because all you're supporting is your own weight, something that your body is accustomed to in the first place. Also, since every part of your "weights" is firmly attached and has sensors, there's less chance that you'll have weights slide off, or bang into the framework, sending you off-balance.
One important thing to do is to not rush through the exercise, even if you think you'll be able to power through one more rep if you do so. You've heard the tales of people lifting cars in a crisis, but injuring their body in the process? Hysterical strength isn't necessarily limited to times of crises and some people draw upon it more readily than others. If you're not paying attention, you may pay that one extra rep with barely being able to move the next morning.
Lastly, don't be afraid to rest between sets. My personal experience is that if I wait a few seconds after completely exhausting myself on a set, I can usually immediately do 1-2 more. If I give myself 30 seconds, I can generally do almost as many in the next set without straining myself. If you ignore rest periods, you're more likely to lose focus and hurt yourself through sloppy technique or dipping into hysterical strength, and you're likely to only get one or two reps at a time anyhow.
As for efficacy, I've had mixed success. I am one of those people who finds it a little too easy to push too hard, so a program like this with a large number of reps, I'm likely to finish it out one night and then have to wait a week to get back to it. That said, I know that it works for other people. It's psychological as much as anything else, "proving" to yourself that you can do that many reps in a single session, if not a single set. Because there's no fixed amount, you're encouraged to continue pushing a little further each time.