If you look at your screen from side to side, if the white dots appear to move relative to your screen, then it is dust. If they don't, then you probably have some dead pixels.
I'm not really sure how you can prevent dust from getting in your screen. The fact that it's there indicates that the screen isn't completely sealed, so one option short of opening your screen up is to find a way to blow compressed air into it, but more than likely that won't help the situation, but simply bring more dust onto your screen.
If you really aren't faint of heart when it comes to your tablet, you can always try opening the screen yourself and cleaning it.