iPad smart cover leaves three vertical bars on screen.

If you look at your Smart cover, there are 3 places where it's thinner to allow the cover to fold up and be used as a stand. Since these parts don't touch the screen, the screen doesn't get cleaned right there. If you remove the cover and fold it with the microfiber side facing out, you can wipe it across the screen for a complete cleaning.

It works perfectly to clean that too. Take off the cover, roll it into the triangular prism, and wipe the screen it works perfectly.

Good question! Mine's not dirty yet. I have the leather one so if it gets dirty I'll probably wipe it down with a damp cloth with some kind of mild diluted soap, whatever I have that will work for leather furniture. I'd imagine the polyurethane would be the same.

When you clost your Smart Cover, it obvously doesn't cover all of the areas evenly. As a result, certain areas may have more grease than others. Unfortunately, this is something that is unavoidable.

I lay a small microfiber cloth across the screen when I close the cover. A couple of quick wipes and it is clean and clear.

Love this forum, this answered my question. Here is one, how do you clean the smart cover?