Can anyone tell me an easy effective way to clean vinyl coated windows?

These windows are on a Florida room. And the vinyl is like a plastic/vinyl sheet that has been put on the windows to help keep the sun out. I have a good cleaner but they still seem to have smudges on them no matter how good I wipe them.

Answers:
1/2 cup white vinegar 2 drops of Joy dishwashing liquid and about a gallon of hot water,, be sure and wash with a microfiber cloth like you can get in automotive at Wal Mart.
Then dry with paper or paper towels.
This should cut the residue.

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