I had a new to me 1995 Intrepid. Same thing, lots of wiper chattering. I put in a used windshield when I got the car, maybe it was contaminated and needed cleaning. I thought being rained on would clean it enough. I forget if I put new wiper blades on but I thought the wiper blades were good, or good enough.
Getting home after suffering a long drive of annoying wipers, I realized that both wiper arms had very little spring pressure and were not holding the blades very tightly to the glass. All of my other cars always had stronger spring pressure.
I think I put on some aftermarket helper springs to put more pressure on the arms to hold the blades tighter to the glass. Everything was perfect after that.