Ever since I started on this hobby of ours, all my turntables had no dust covers. So when a friend who bought his first turntable asked me how to clean a dust cover without leaving any hairline scratches, I couldn’t confidently give a good answer.
Whether you get micro scratches or not will largely depend on the material the cover is made from unfortunately. Dust itself is enough to scratch cheaper plastics so the softest cloth in the world won’t matter.
Use the softest micro duster you can to prolong the inevitable but don’t lose sleep over it.
No matter how careful I am, mine picks up a fine haze over time. About once a year I clean it inside and out using Novus polish and a microfibre cloth. It comes up really well, maybe better than new.
There are 3 grades of Novus, and 1 is usually sufficient. If there are visible small scratches or scuffs, I’ll first give it a going over with no. 2. There’s also a no. 3 for heavier scratches, but I’ve never needed to use it.
Echoing @feeling_zen’s post above, Linn’s care advice for the LP12 cover is:
Lid
The lid should be cleaned with a soft duster. Remove any stubborn dirt or marks with a soft, damp cloth, then finish with a dry, soft duster. The lid can be very easily marked so avoid any harsh rubbing action. Lids are more often damaged through over-enthusiastic cleaning.
In first istance use a dust cover, a cotton cloth or microfiber, i always did so on my turntable and you virtually don’t need to dust it. Whenever you have to clean it, may be every few years, give it a nice spray with distilled water and some cleaner like Permanon Glass or something used for screens, applying the slightest pressure with microfiber. My Rega P3 cover 14+ yo is pretty much like new.
My solution for the last 10+ years is spraying the dust cover with antistatic plastic cleaner and wiping it dry with a very soft cloth. I basically drag the cloth over the surface, instead of scrubbing it.