I think there are a couple of genuine stars in there, but I think most of the small dots may be damaged pixels from cosmic ray hits. Some guys from Johnson told me last year that they periodically have to discard and replace cameras because of accumulated radiation damage, so this might be it.
I think the astronauts could compensate for these to a limited extent by regularly taking dark- and flat-field images to determine where the bad pixels are, but apparently they don't do that.
I wonder what this does to the sensors in Hubble. It's in a lower inclination and slightly higher orbit that would accumulate less radiation, but it still accumulates some.