Thanks to a mention from Colleen in a comment, I am now aware that my RSS feed is messed up. I totally screwed up my prior RSS feed and thought going to a default template from the EE site would fix things for now. Apparently, though, if I edit a post for any reason, it shows up more than once in a reader. Great, now I've got to worry about this. Like I've got time to deal with it.
Edit: Also figured out my permalinks were wrong. Weeee. Testing to see if this fixes the problem.
Edit: Also figured out my permalinks were wrong. Weeee. Testing to see if this fixes the problem.