If your stage floor is not sprung, then it should be a priority to have it replaced with a properly constructed floor that will work for your productions, dance, and other general uses. There are many ways to construct floors that will last and be functional, so enlisting an expert (like a Theatre Consultant) that has experience in this area can be very helpful. There are many possible materials to be used, and each has advantages and drawbacks. Knowing what works, and what doesn't, can save money and injuries.
Another dangerous item on stage is old footlight troughs. If they are not locked and you step on them, or maybe set a scaffoding leg or man-lift outrigger on them, they can fail or flip-over. Equipment and people can topple and cause major injuries and damage. This blogger knows of at least one dance instructor that had a career-ending spiral break of the leg bones that left them out of work for months and will never be able to dance professionally again. That's serious stuff!
ANSI E1.26 - 2006 - Recommended Testing Methods and Values for Shock Absorption of Floors Used in Live Performance Venues - http://www.ansi.org/
Dance This Dance That Blog - www.danceartkl.blogspot.com/2005/09/5-common-dance-injuries-how-to-treat.htm
Harlequin Floors FAQ - http://www.harlequinfloors.com/uk/dance-area/about-dance-injuries.html
Center Stage FAQ: http://www.centerstagellc.com/health/importance-of-proper-dance-flooring-injury-prevention-dancer-longevity/