Haze on inside of windshield

I have recently inherited by father-in-law's 2000 Intrepid, which he bought new. I would tease him about not being able to see out the windshield due to a haze on the inside of the glass -- it looks a lot like smoke residue. Now that I have it, I realize that I cannot get rid of the haze; unless I really really work at it, window cleaner just seems to smear it around. Even if I do get the glass clean, it is back within 24 hours. I would assume that after 4 years, the dashboard, defroster ducts, etc. would have finished outgassing, so I can't figure out what this stuff is, how to clean it off, or how to get rid of it permanently.
Anyone else have any experience with this problem, or any suggestions on how to deal with it?

Thanks!
Mark

I had a similar haze on the windshield of my old 1994 Eagle Vision when I bought it. I just used 409 all purpose cleaner, it's purple, and some newspaper. That took care of the problem. The film returned soon after but after cleaning it a few times the film came back less and less frequently.

Mine sure hasn't been returning with less frequency! It begins to appear within 24 hours -- and this is a 4+ year old car.

Ghosts.

You could also have a leaking evaporator core. It did that with my 2004 Dakota.

WHen I have had that problem, it was coolant seeping from the heater core.....