Windshield wipers chatter and skip even though they are new? The reason is your windshield is dirty! Yeah, we know you cleaned it with Windex after washing the car, but it's still dirty with an invisible film of road salts and oils. This film must be scrubbed off. The best thing to accomplish this task is Bon Ami cleanser, still found in its original 1940s-style can in the supermarket. Wet down the windshield, liberally sprinkle the powder and scrub with a soft-bristle brush (you know, the kind your Grandmother used to scrub the kitchen floor with). Rinse thoroughly and dry off with paper towels. You can clean older wiper blades the same way too, since the films accumulate on them as well.
Tip for this tip: Do this before washing the car to avoid mess.
2nd Tip for this tip: Don't (repeat: don't), use Ajax or Comet or any other chlorinated or pumice-containing cleanser. If you do, you're going to have to learn how to re-polish the windshield glass.