I don't have this issue with my previous HX9V.
On my HX60V photos taken on any setting, as long as it's ISO 400 or 800 I get many white spots in dark areas (no flash used)
The bright white spots don't appear at ISO 80, 100, 200, 1600 or 3200 only 400 and 800. I did reset the camera but didn't make a difference.
If someone else has a HX60 camera I would be very grateful if you could see if this issue is on yours, if it is then it may be a software issue as it only appears at two specific ISO settings.
Put the camera in manual, exposure 1/1600, ISO 400/800 F8 (no flash) so that the image should be 100% black and check for white spots, mine looks like a starry night sky.
This issue is not on the older HX9V, same settings on that camera and every image is 100% black with not a single white spot, even my iPhone doesn't have this issue.
Here are the images from ISO 80 to 3200, the two normal photos are ISO 800. You will need to download the original photos and zoom in to see the spots.
Have zipped them up and uploaded them here.
https://mega.co.nz/#!vMdywQ6R!6s7VaSPKqk4PbPMqZMqZUvF3cSBNIZt-iZYKgT1_IPA
