I keep reading, including on Wikipedia, that the main character, Don Draper, was in the Korean War, even though I was under the impression it was Korea in World War II.

I thought I'd seen the date "1944" written in a subtitle during a particular flash back but now I can't remember what episode it might have been in. It wasn't in the flashbacks I just checked.

The timeline seems like it would be really messed up if he should have been in Korea - lots of inconsistencies with references in a lot of episodes. However if the war the date is actually supposed to be 1944 it all fits pretty nicely.

He's supposed to be 36 in season 1 which is in 1960, which would have made him 20 in 1944. His brother would have then been 24 in 1960 as his brother said he was 8 when he last saw Don. This also gives the character some time to do the things referenced (and shown) in the later seasons, such as take night school college courses, work at a car dealership, move to New York and work at the fur store. Al before being hired at Sterling Cooper and having been there "10 years" as I recall also being referenced in season 1 or 2.

The odd bit out is that in the first war flashback, his commanding officer makes a remark about him not mistaking him for the Chinese. This would be more apt to the Korean War, as he should have said Japanese for WW2.

The Korean war went from 1950 to 1953 and really makes a mess of the timeline. Even if he was there in 1950, it means the brother character would only be 18 in 1960 - they should have cast a younger actor. It means that there's no way that he could have been at the ad agency for 10 years in 1960/1.

Just seems like sloppy continuity/background work on a show that's otherwise really solidly put together.