Q -- your link doesn't work. I also found a link to a short film by that name on YouTube (see below). I wonder if it's the same one:

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Here is the section from Wikipedia that mentions the tooth mouse -- though, as noted in the header, the article does not cite any sources. Perhaps we could get a Mudcat squad on the case?

In Spanish speaking countries (according to this article), the character is known as Ratoncito Pérez, which is actually "little mouse" Pérez (not quite the same character to scare the neighbor kids with as a giant rat, but...).

Putting the Spanish name into Google, the first hit I got was to the Spanish version of Wikipedia. As I read it through the computer translation, it looks like the tooth mouse was actually a literary creation from the end of the nineteenth century, by a Jesuit priest. Though he might have just been putting down, in literary form, a vague folk belief that goes back much further.

I did find a YouTube video called "Ratoncito Pérez," about the tooth-buying ritual, though the mouse himself doesn't appear.

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McGrath -- I actually like rats, and think they get a bad rap (though I think a giant one would give me pause). But even a giant rat is preferrable, to me, to the trend (at least among American advertisers) to show the tooth fairy as a fat, middle-aged, un-shaven and surly man in a tutu and fake wings. That's just being clever and contrary for the sake of it.