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.
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".
I think the referring to "a Japanese" vs "a Japanese man/woman" sounds a little racist, it shouldn't, it makes syntactical sense, but I guess its the cultural influence on the language, I don't know why I brought it up, I was just really taken back when you said "I'm married to a Japanese"
It really does sound strange to me as well, almost derogatory in tone. It sounds so much better to my ear to say "i'm married to a Japanese person" or "... person from Japan". But I have no good reason as to why the same doesn't hold for Canadian/American.
Thanks, I think I'll have to keep that in mind when talking in English. The thing is, I thought about writing 'Japanese woman', but her gender seemed besides the point to me, so I didn't want to mention it. In my native tongue (German) there is no unisex term for nationalities, you're either a "Japanerin" (= Japanese woman) or a "Japaner" (= Japanese man). Because of that there might be less subtext when talking about nationalities, but I think this is all just due to the history of your cultural relations - for example in Switzerland there is some negative subtext to the word 'Yugoslave', because their immigrant group was rather unpopular at one point.