Long story short, it falls under the "easy come, easy go" category. Whatever progress you make fast, can be lost equally fast.
Losing a lot of weight is more than just losing a lot of weight
Really, there's no problem with losing weight in short bursts, but you have to keep a pretty strict diet in between those bursts too, if you're not going to gain the weight back again. And then you're on the "minor adjustment, longer period of time" after all, so why not do that from the get-go?
The reason why small adjustments are better, is because your body needs to adapt to the changing circumstances. Your spine might get some much needed relief, your muscles might suffer some loss, your hormonal balance might change, your cholesterol, blood pressure, blood sugar, sleeping pattern... I could go on and on.
These should not be subject to overwhelmingly rapid change. The most notable exception is if someone chooses to undergo elective surgery, such as gastric bypass. But this is the most drastic measure one can take, and is done under very close supervision by medical professionals.
Is it much harder to maintain a constant weight after extreme dieting, than after a moderate diet?
Exactly the correct question, and I think I've said most of what needs to be said here. Yes, it's harder. However, you could get a medical check-up, and get some feedback from a doctor. It's still doable. There's just a lot more you need to be aware of.
Should I expect certain health issues because of such a diet?
Your diet should be meticulous no matter what you're trying to accomplish. Even someone who isn't making weight changes should endeavor to fill their quota of all the vitamins, minerals, and other essentials that the body needs to function properly.
A weight loss diet has to be even more carefully planned, because you have to cover all your quotas over a smaller caloric intake.
As long as you have this down, there's no reason why any diet would cause you harm.