Haven't had this problem with ours, Dec 2000 with 125,000 miles on the clock. However, particular cars can suffer individual problems so I would guess yours has either had worn out blades or a problem with the mechanism/arms/springs in the past.
I've also seen scatches on windscreens caused by wiping the screen when it was dry (i.e. leaving the wipers in the on position when switching off the engine in the rain and then re-starting the engine later when it's dry).
If the polishing doesn't work you might need a new screen.....