I've used muriatic acid to clean both acrylic and glass tanks on at least a dozen occasions wth absolutely no ill effects. I also regularly use it to clean PVC, pumps, and just about anything and everything else in my tank. Don't use it straight. You don't need that much acidity. I've found between a 1:10 and 1:20 acid to water solution works very well. And yes, you can mix it with water. Just be sure to do it in an open area, and don't stick your nose in the bucket as you do it, because it will release a noxious vapor. Also remember that rhyme from high school chemistry class, "Do what you oughta, add acid to water". In other words, water first, then add the acid. I'd recommend using gloves (especially if you have any open cuts), and safety goggles are a good idea as well. Pure muriatic acid will burn you, but it's not going to "eat your flesh". The solutions I'm talking about may cause skin irritation with some people (I've never had a problem personally), and will definitely burn if you get it in your eyes.
Vinegar is a tried and true solution as well, but not quite as effective, and for a larger tank may start getting expensive. A 50/50 mixture of vinegar and water is usually going to work well enough, though, especially if you let it soak for a bit.