Oh, was Mike actually being a drunk baby on the giant flask episode? I just always assume it's acting.
IIRC, they started with Half in the Bag where they'd watch movies sober in the theater, and then drink in the studio while filming. Their collection of empty-bottle props was legitimately what they drank, they just started keeping all of their empties to use as props to make it look bigger than it really was.
Jack confirmed during some of their Pre Rec streams that he drinks casually while playing videogames, because people in the chat have asked him for details of what exactly he's drinking.
They drink while watching six hours worth of bad movies for BotW, and then drink more while sitting around for another few hours talking about them. I think they said that the Star Wars Holiday Special was the drunkest they've ever been on the show.
AFAIK, Jack's wife doesn't like it when he comes home drunk, so he doesn't drink irresponsibly. Rich Evans is concerned about his health, so he's trying to clean up his act. Jay doesn't seem to go crazy with it. Mike is the real boozehound of the group, and it's only gotten worse since Jessi ran off to Venezuela.