Over time the flapper - which is soft and supple new - becomes dry and hard. Replacing the flapper will normally fix a dripping issue, and it's about a 5 buck repair.

Well, I have never done it, but the screen on the DS is plastic, and I repair scratched and foggy car headlight lenses. If they are really fine, a small buffer and a tiny drop of compound wax should do it. Be sure to tape off the screen so that you don't buff anything else. Best of luck!