Today I finally had it with the scroll wheel on my wacom mouse constantly slipping so I decided to do something about it, this is how I fixed this problem. In order to do this you'll most likely need a small knife, a screwdriver (Philips IIRC), some spray-on glue and something small to apply the glue with.
There are three small screws that you need to remove in order to open your mouse, one in the back and two in the front, and they are all covered by the felt mat under the mouse so you'll need to remove it. Removing the mat should be done carefully using the knife, only lift enough of it to ensure easy access to the screws, when you've removed the screws you can put the mat back for now.
The problem I had and which I've noticed in a couple of other Graphire 3 mice is that the rubber "ring" that you spin with your finger is no longer stuck to the plastic wheel inside it tight enough. The easy solution to this problem is to push the rubber ring to the side and then smear some of the spray-on glue in the plastic wheel before pushing the ring back on and making sure everything is working fine. Remember to smear glue all around the plastic wheel so that it won't come loose again really fast.
That should be it, just put your mouse back together again using the same techique you used for disassembling it and you will hopefully no longer be plagued by the scroll wheel not working.
Also, if you have problems with a mouse of some other type I highly recommend Repair4Mouse where you can also find a link to this article. There is also more information on fixing broken Wacom mice over at www.beeldbuijs.nl.