The FZ10 has fantastic zoom range, but a fairly average built-in pop-up flash. As a result, flash performance may be disappointing, especially if you are working in telephoto ranges. Even external flash performance may be disappointing. Other than using a slave flash which is closer to the intended subject, another option is to try a flash extender...
strat (FZ10 gallery) (Yahoo!, FZ10 forum, 7 May 2004)...
Even the Canon Rebel and Nikon D70 with their pop-up flashes can{not} `reach' more than 10-15 feet. Sometimes a bit more if there are good reflective walls but generally in a gym or auditorium the walls and ceilings are too far way to be of use. I don't know the range of the accessory flash available for the FZ10 but it certainly should be better than the built-in flash. The nice thing about the FZ10 for your purposes is that it can also take flash units made by others. Some digicams can't. It all depends on the voltage limitations of the camera and that of the flash. You might want to look at George Lepp's Project-a-flash.