[archangel_one]

Does to me; I guess I think of it as either an adjective or referring to the language. While this usage is technically correct, I think I'd always say "Japanese person". I don't really have a good explanation though of why it's different to "American" or "Canadian" in that regard. Maybe just it's less common for some reason.

[thaumasiotes]

Personally, I don't have a problem with the form "I'm married to a Japanese" (this usage comes up a lot for me, although I'm generally referring to Chinese rather than Japanese). But if I were to avoid it, I definitely wouldn't say "I'm married to a Japanese person". I'd say "My wife is Japanese".