I'm not an instructor, but I would consider myself an expert in falling :p Here are the things that I do to avoid injury when something goes wrong:
1. The obvious one is cushions around the pole when learning new tricks, of course
2. Cling to the pole with whatever you can! It will either stop your fall, and buy you some time to figure out how to untangle yourself and get down, or at minimum slow you down enough to reduce the impact. A fall flat onto your back could be a disaster from 5 feet in the air, but from 1 foot, it's just kind of embarrassing (that was me in class last week after my stupid sweaty hand slipped off the pole in an aysha).
3. Never let go with your hands! If a hand is on the pole it's just about impossible to land head first. In tricks where you're meant to let go of your hands, make sure you know how to regrasp the pole with them if needed.
4. Before you try a new trick, think about the "escape routes": how you might fall and how to prevent it. For example, in a gemini you might lose leg grip, so practice taking your hands off and then putting them back on and lifting your chest and head up a little. Practice this a few times so if you do slip it's automatic to regrasp the pole with your hands.
5. Practice emergency escapes. Work on going from any inverted trick back to a basic invert (with hands on the pole), or any upright skill to a pole climb position. You could also try inching down the pole one limb as a time from a basic invert - this came in handy once when I got all tangled up on a spinny pole going way too fast!
6. Tuck your head down towards your chest. If you are going to end up head first, this is the best way to minimise damage. That's not to say you wouldn't be hurt at all (I once landed head first on a trampoline from great height. I pulled several muscles in my neck and got a badly bruised sternum, but if I didn't tuck my head in it could have been a broken neck!)
7. Never land on an outstretched hand (I broke my arm as a kid doing this. Never again.) If you're falling to the side land on your side with your bottom arm straight and palm down just in front of your thigh (if that makes sense).
8. Of course, all of this is kind of hard to actually do once you're falling! Just practice what you would do in a fall, and try to stay calm (if that's even possible). And be safe to prevent falls too!
So that's what I've learned from experience. I'm sure some instructors on here would have plenty of useful stuff to add, or maybe even disagree with me!