Turntable dust cover cleaning

Seems to me that whatever you are using to "clean" is the cause of the residue in the photo. I have used Sprayway myself for windows and it is far from streak-free. You might get better results with a mild solution of distilled water and white vinegar.

For windows, I spray the window and then buff it dry with newsprint (yes, newsprint), but for the turntable cover I would use a soft, liny free cloth like one used to clean computer screens.

Not sure why all the talk about swirls, when that isn't the issue.

Thanks all for the feedback and advice. There are a couple of suggestions I'll try here regarding cleaning solution and microfiber cloths. I'll report back on results. And, as several have mentioned, it is not a scratch issue as the cover is in perfect condition. It is very much about the film that is a result of both the static from the dry climate, and perhaps use of Sprayway. I have a "Hudson Hi-Fi Vinyl Record Cleaning Arm Anti Static Brush" that will move around when I'm running a cloth over it, from the crazy amount of static. 

@hazeloop are you saying that your Hudson HiFi anti static brush (under the dust cover) will move around when you’re running a cloth on the outside of the cover?

Use Novus #1 "Plastic Clean and Shine", and you'll never look back.

Once you you get it clean, just use a very slightly dampened microfiber cloth with distilled water.