If you can get hold of a suction cup (they are pretty cheap on eBay), you can pull the glass panel off - it's just held in by magnets. You can also try the tape method:http://www.youtube.com/watch?v=cy0o2WdrN3M
or even the plunger method:http://www.youtube.com/watch?v=4Xh4Ip87hPE
If you go the plunger route, remove the plunger before putting the screen back on. If you decide to remove the glass, remove it very carefully as there are little pins that can get broken.
You can even just pull the side a little to see if the stains are attached to the glass or the panel. If it's on the panel, try poking your finger in to see if you can wipe the stain away. Try not to leave obvious fingerprints behind though.
edit: Here's quite a good video guide for removing the glass:http://www.youtube.com/watch?v=9cHMH...eature=related