That's a pretty big picture you posted. Think next time you ought to shrink it down a little.
As for the white dots, it's probably hot pixels inside your CCD if I'm not wrong. These happen frequently on shots that were set for longer exposures. The only way to get rid or minimise this effect is to set a lower shutter speed or go remap your camera.
Another way to reduce the impact of hot pixels is to take a dark frame shot (i.e. no light) using the same exposure settings and at around the same time as your actual photo. This will isolate the hot pixels, and you can then subtract this image from the actual photo in an image editing program to clear up the hot pixels. This can be rather troublesome though, so you might want to do this only for "important" shots. Some high-end digital cameras have similar algorithms built-in directly.
Btw, to SpaceMonkey, your problem may also be due to amplified CCD noise if you are using your camera's higher ISO settings. Perhaps you can try fiddling with your exposure settings to see what gives you the best result.
p.s. A tripod or some other form of firm camera support will also reduce the blur due to camera shake at slow shutter speeds.