That was my same impression, I don't really care much for them. Try to clean the cover with a lint roller, the tape looking think and see if my cleaning the inside of the cover it will improve for you. Some people say that help.
iFrog's suggestion to clean it with a lint cleaner sounds like a good one which I will test immediately. Though I don't use mine all the time, I find that if you fold the cover with the lint side in, it won't get nearly as dirty. Also, if you really don't like it, Apple will sometimes take it back long after the return deadline. I almost returned mine, one of the people at the store told me to bring it in, but I decided that I did like it after all.
Six days later and I haven't seen the lines yet, but I definitely want to invest in a lint roller to clean the cover in hopes to be preventative. I like the cover other than the fear of streaks.
The inside of my folio case is also made of a somewhat softer but similarly textured material as the Smart Cover micrfiber. It also picks up dust here and there if I'm not careful. Lately, I've begun laying napkins over the iPad screen when I move (in between the screen and the microfiber) and it keeps the screen looking *very* clean. Napkins are inexpensive, reusable, and available almost everywhere.