If possible, try to land on the mattress with both feet flat and knees slightly bent. This helps absorb the impact of the fall. The mattress may be soft, but it's not almighty. If you land with your feet in weird angles, you may end up twisting or spraining your ankle. If you land with your knees straight, there's a high chance of you damaging the knee ligaments (correct me if i'm wrong, life sci majors).
When you're jumping off the end tile or any tile, don't just jump off happily without looking at whats beneath you. Look out for gaps between mattresses, shoes, chalk bags or hard objects. These are potential hazards waiting to claim their next victim. Land with bent knees and feet flat on the mattress.
When you are making a risky move, always prepare yourself mentally that you may fall anytime. This gives you the awareness of where you are, whether there are any safe landing spots below you, and the position that you are most likely to land on the mattress. You can then anticipate the fall if you fail to make the move, and adjust your legs accordingly.
In the event of slipping off footholds or handholds, you may not have enough time to react to the fall. If you can, try to land on your back with your legs away from the torso. I've been hit at the jaw by my own knees a couple of times. You may get bleeding lips or worse, a sore jaw (I have one now). And do bend your knees.
And lastly, always check if there are people behind or beneath you when you are jumping down or climbing. You do not want to injure anyone, including yourself. This has happened in the gym before.
Hope all these are useful tips. Everybuddy, please add on to whatever I have pointed out to everyone's benefit.
Climb safe, train safe, land safe.
Praying for a fast and complete recovery for all sprain victims.