I've searched the forums and found that I'm not insane. Many other people have experienced this problem, and no one ever finds a solution.
I've used many different versions of WordPress on many sites and switched themes on them from time to time. I can't even tell you the pattern of events that causes the problem because it just seems to happen randomly. Perhaps it's during upgrades, or switching themes.
But this happens on ALL my WordPress sites on multiple domains (and no, there's nothing wrong with the server):
The ends of sentences (possibly double spaces) constantly are replaced with the character "Â"
I'm sick and tired of going in and fixing dozens (or more) posts every time this happens to a customer of mine (or my own blog). I'm not doing it anymore. If I can't find satisfaction, I'm stripping out all of them and replacing them with other blogging software, banning the use of WordPress on my server forever.
Harsh? Maybe, but I'll do anything for satisfaction at this point.
I want to know how to get rid of the character NON-manually, and how to prevent it from ever happening again. Is that too much to ask?