I think it would also be interesting to share some ideas on avoiding those spots.
When the spots are in different places on each frame as it seems to be, it's dust in the air combined with a flash too close to lens. The strong light near the flash makes the particles visible and the closeness to lens front makes them very out-of-focus and therefore blurred bigger than they really are.
Using an external flash would avoid the spots, unfortunately most compact cameras do not have any means for connecting one and while using one off-camera is still possible (by using manual mode, an optical slave and shielding the on-camera flash), it's too awkward and inconvenient in social situations where a compact camera is typically used.
Sometimes it might be possible to find another place with less dust or more light so that flash would not be needed.
You could try holding a credit card between the flash and lens as a shield keeping the flash from lighting the immediate front of lens; when doing so, check that the lower part of photo is still correctly illuminated.
Bouncing the flash away (using a reflective surface) or using a diffuser might also help. In those cases, maximum reach for the flash will be shorter.