In the very first scene Archie comes downstairs and Edith makes the joke to let him know his fly is open, but several times we see the front of Archie's pants and clearly his fly is not open.
Harry claims to have tended bar at Kelsey's for ten years, but he was never seen until the previous season. Prior to that, we've only seen Tommy the bartender (played by Brendan Dillon) and Kelsey himself (played by Bob Hastings).
Archie told Mike to serve the two "Wallbangers" in dark glasses, but Mike uses regular transparent ones.
Although a top- notch bartender with at least ten years' experience to his credit, Harry still needs his bartender's guide to make mixed drinks.