Over time, the inside of the iPad’s Smart Cover attracts dirt in the recessed fold areas, which then tend to deposit in ugly lines of grime on your iPad’s screen. Similarly, the cover itself starts to get dirty. If you have a back cover on your iPad (like the cover that I bought & modded), it too will need a cleaning from time to time. For all of these, the solution is simple – any of the common iPad screen cleaners and a microfiber cloth will do a very nice job on all of the covers – and in the case of the Smart Cover, will make it look practically brand new.
By the way, you can generally save yourself a little money and get a common HDTV screen cleaner for $15 for a huge bottle instead of a tiny bottle of iPad-specific cleaner. I use the same HDTV cleaner to clean my HDTV and my iDevices. The one exception: When I am on the road, I use the Monster CleanTouch (available in many electronics stores, Target, Wal-Mart, etc) simply due to the very small footprint of the container, which fits nicely in my tech backpack. When it’s empty, I’m going to see if I can refill it with HDTV cleaner and have the best of both worlds.