In Mad Men Episode 6.11: Favors, Don comes home to find Megan talking with Mitchell Rosen. Mitchell leaves and Megan explains he’s 1-A, draft eligible. Don asks how that’s possible if Mitchell is in college. Megan says he sent his draft card back in protest, so they reclassified him.
Later that night, Don and Arnie Rosen drink in a bar, and Arnie tells Don he didn’t even know his son left college.
Which is it?
I don’t think this is a continuity glitch. I think this is a dishonest young man who’s been telling stories left and right.