I have been inundated with questions and queries about how I took apart my iPod mini, how I replaced the click wheel, where I purchased the click wheel, the current status (ie, did it work?) etc. For the sake and service of the greater good, I'll attempt to shed a little more light on this subject than I did in my original post...
First, to take apart your iPod mini, there are a number of resources out there, but the one I used was here. They've got step-by-step instructions, pictures, etc. They also appear to do this kind of stuff for a profession, as opposed to some yokel that just wanted to yank his mini apart (iPod, that is).
Caution: I take no responsibility if you make the same or similar stupid mistakes and wind up doing what I did (or similar, meaning breaking) to my mini. There are trained professionals that can assist you if you don't want to risk having to pony up money to purchase self-inflicted repair incidents. More on those people later.
Second, I purchased my click wheel on eBay. Predictably, if you'll use eBay's search to find “click wheel”, you MIGHT turn up a seller. However, I've not seen many since my purchase. On the other hand, I don't really have a need for another wheel, so I've not been looking real hard either. But in any case, like for most things, if you need it it's probably on eBay.
Another word of caution: I ended up purchasing my click wheel on eBay for more than the total cost I was quoted plus the cost of shipping to have the replacement performed by one of my aforementioned professionals. Unfortunately, I had already committed to the auction, and I'm not one to try to renig from them.
Third, about the previously mentioned iPod repair professionals. I know for a fact that there are many folks that advertise services to repair, replace, service, upgrade, customize, etc iPods of varying generations. You need to make sure that whatever group you pick, they service your particular version of iPod. I had a few conversations with iPodMechanic. You'll probably have to contact them first to describe your need, get a quote, etc, as they don't have “Replace click wheel” on their repair page for the mini.
Finally, since I performed the wheel replacement myself, it's reasonable for some of you readers to wonder if I managed to be successful. It appears that I have as I've been using my mini regularly (and I'm a very heavy user) since my replacement occurred over 2 weeks ago. Thus far, it's been as if I'd never screwed it up in the first place.