Sounds like hard water.
Here is a link, check out #28
http://www.applianceaid.com/dish.html

Has it always done this or is it something that just started recently?
Is it just the film or is it also food particles?
Has anything changed in the house plumbing lately re: new water softener etc.?
When you tried a different soap, did you try a granulated type?
Note: In my opinion this is still the best detergent.
Have you tried using less detergent?
Is the water entering the unit a minimum of 120 degrees?

I would also try emptying some water out of your hot water tank.
Use either the drain or the over pressure release. Let it run till it is clear.
Minerals etc. can collect in the bottom of the tank.