Yeah, I also noticed some lines on the top screen where it touches the sides of the bottom screen when closed. Makes me wonder if they did any testing to see if this design was such a good idea, because it took a day to realize that it wasn't. Oh well.
For anyone who doesn't have or want a screen protector, just do what I do: stick a piece of packing material between the 3DS when you close it up. The system came with a piece already in it, which is what I use, but if you don't still have that, I'm sure you could cut a piece out of something else you bought recently.