Sorry, me again. Got Facebook Like up and running, having fixed the "Grant Extended Permissions" thing.
It worked well for a while, I'd thought. Got a handful of "Likes", but then noticed that they weren't showing up on these people's walls at all. I went and checked the API codes, and realized that my API Key had been wrong, from my futzing with it over that other problem.
So, I fixed the API Key, and now the Like button doesn't work at all! Please advise.