Not sure about the white eyes, unless it's just lack of detail from being so far back, but you have a pretty long zoom, so you should be able to get a reasonably tight shot. OTOH, that little popgun flash is only going to be effective to 17 feet. The stage is probably that deep, and if you were in the back of the theater, you were probably not that close to the stage. But the air between you and the stage was well lit.
So, bottom line, your flash had zero effect on your shots (unless that's the source of the white eye). As for the basic exposure, assuming ISO 64 or 100, you probably didn't have enough light to keep the shutter speed fast enough to prevent camera shake, hence the blurry pictures. The long telephoto contributes to this problem. The theory is, take 1 over the 35mm equivalent focal length (380mm for your camera) and you have the shutter speed to prevent camera shake. Even at your maximum ISO 400, you probably aren't going to get that shutter speed, so you have to get closer and perhaps use a bigger flash. There's two problems with that. One, ISO 400 is going to have a lot more photographic noise, making any resulting photo less attractive. Two, flash is pretty uncool when everyone else is trying to watch the play, even more so for the actors.
Point and shoot cameras are just not designed to handle this sort of situation. Even dSLRs like my Nikon D70 or the Canon 350XT can be at the limit of their performance to get this sort of picture, especially if you don't have very expensive, high performance lenses. My camera has much lower noise at ISO 1600, and the Canon is even better in this regard, giving this type of camera a much faster shutter speed.
Cheers,
Eric