I've used one of these.
I don't know about fast shooting.
If you push the shutter button and take a picture, the camera goes away and starts thinking. It's quite some time before its ready to take another picture. I even tried reducing the resolution to its minimum thinking that this would mean less data going through the camera, but it seemed to take just as long.
I just recently starting take pictures at my daughter's cheerleading competitions. (She just started doing this.) I'm using my Nikon D5100, which even though it "only" goes to 4 FPS, I'm still firing off 200-300 shots within their 2.5 minute routine. Having used the Nikon P500, I don't think it would keep up with that. I believe I wouldn't get as many keepers if I was using the Nikon P500 (or any point-and-shoot for that matter) So as far as that comparison to a dSLR, I don't think it compares on that point.
But playing around with it, everything else seems pretty good. The shutter lag isn't as long as all the point-and-shoots I've had. Its actually quite good as far as point-and-shoot. Focus, in low lighting, is a bit slow, but at least its able to do it, which some aren't able to focus at the long end. The focus and colour when using the camera on green automode (and the other automodes for that matter) all turn out really nice.
I've seen these cameras on sale for $300 or so and I've been tempted. But I've already spent way to much on camera gear over the past year or so.
The biggest difference (for me) between the Nikon P510 and the Nikon P500 is that the Nikon P510 is supposed to go to ISO 6400. (I don't know. Maybe the Nikon P500 can be pushed to ISO6400 as well. I didn't have that long to play with it.) For me, personally, ISO6400 seems to be the magic number that makes a camera fun to use for me.
Please don't mind the swirly faces, as my daughter is calling it.
My daughter just woke up and she wants me to put a swirly face into the message.
:lmao:

Ok. Got to go.