Well, as far as I know, this issue is now resolved. Thank you guys so much for the prompt and helpful suggestions.
I ended up taking the damn thing apart and removing whatever gunk I could see near the mousewheel area. After cleaning it as much as I could, I put it back together, and the problem has now seemed to have vanished.
The timing of the glitch really made troubleshooting a nuisance, as it happened RIGHT when I upgraded to Windows 7. So, I automatically assumed Windows 7 was to blame. It wasn't until I moved the mouse to another computer that I discovered the same problem while scrolling up and down on a particular page.
For anyone that might be looking for a solution to this sort of problem, hopefully this post shall serve as your beacon of hope.
I was also aided visually by the photos posted in the following thread at Tech Support Forum: Anyone opened up a Logitech MX518 Mouse? - Tech Support Forum
Again, thank you guys for the help!