Hello!
My first question would be : was there smoke on stage? This might be the explanation of what we're seeing. Maybe the strong lights saturated parts of your sensor, also.
I think these results are pretty good for a compact at ISO 1600! Very nice, indeed. Noise generated by the sensor probably accounts for some of the effect you see. But since it didn't happen on all pictures, I would tend to blame the lighting conditions onstage.
for concert photography, in general, the larger your sensor the better your images will be, because you will want to increase the ISO (as you did). That means a DSLr would be a "better" choice, but also a more expensive one. And a more cumbersome one. The decision is yours, and I think it's great that you experiment with various models. That way you'll get the best camera for you.
by the way, regarding settings, your digital files retain the information about your shooting parameters in the EXIF data:
http://www.digicamhelp.com/glossary/exif-data/