What about a conviction maybe 15 years ago for shoplifting (misdemeaor--no felony)?
Considering how much Koreans I know drink, and how close EFL teachers I know come to being alcholics, I doubt that a DWI is going to be that big of a deal. If it comes up, just say you made a mistake and learned from it and have never done it since.
A misdemeanor on a record didn't keep one guy I know out of SK. He was welcomed with open arms. Maybe it was because he had a real degree and a real TESOL. Not sure. But if they said "Yes" to him, they will probably say "Yes" to you.
Best of luck to ya.
I do know they make background checks when you go and teach. Does something like a past DWI cause a problem if someone wanted to work in South Korea? It is considered a misdemeanor in the U.S. So I am not sure how I can find out if I would be barred from working due to that or not. Feel free to e-mail me if you want, if you have any information.
B.K.