I ended up fixing the problem while speculating on possible causes on the support forums. I should have just done that in the first place.
I had installed a mod to convert quoted images to a URL instead of displaying the image again (ever see those run-on threads with quotes of quotes of quotes, each with an image, thus displaying twelve copies of every image on the same forum page? Yeah, me too. I hate those. That's what this plugin is supposed to fix.). Needless to say, the mod was malfunctioning. It's not supposed to throw an error every time a post is made that contains BBCode.
Oh well. Good to know it's fixed. I guess we'll just have to not quote images, or snip/link them ourselves when quoting.
Ugh. 3 AM on a worknight. I really need to stop doing this. Goodnight all!