Hi bobdob,
Sorry, I thought you were South Korean at first...
I recall an American citizen applying for a work (business?) visa in Japan and found nothing about a criminal record investigation in it. The visa review process is more lax for foreign nationals married to Japanese. I think that that kind of investigation comes only when you apply for permanent residence or naturalization.
Even if the authorities do investigate, it will be in your home country, I think, unless you have lived in South Korea for a very long time. The only possibility of getting caught will be to be on the "persona non grata" list, i.e., criminal record in Japan.
My personal conclusion: Very low possibility of it hurting your chances.
I have found that the only countries that consider adultery a crime are South Korea and Taiwan. A Korean newspaper on the Web had an article saying it is high time the nation did away with this law. Adultery was a crime in Japan before World War II. McArthur scrapped it for us.
Hope it helps in some way!
PS I forgot to add that adultery in Japan was a crime for women only!! :box: