In my mind the Immortals probably have some sort of long-term healing mechanism as well as the short-term one. It would be necessary just to protect an Immortal from the kinds of diseases that they would contract, just looking at the statistics of disease at various times; I mean, even ignoring plagues and such, it would be pretty much impossible to live for five thousand years or even a few hundred years cancer-free, unless one had some kind of defense and/or way to beat it kind of...automatically, I guess? So assuming the latter option, perhaps...uhm... dental damage would heal itself as well, once he had his first death?