What we woulda said back then
Though I love the show, I don't personally care about the "authenticity" of the language in Mad Men -- "authenticity" being a lost leader, I think, realism a red herring for critics and viewers and apparently Matt Weiner too -- but John McWhorter and Benjamin Zimmer's clear critique of the language's historical accuracy brings up, I think, two interesting problems:
1. If it were more authentic, it would feel less so.
If Mad Men actually were a show where people spoke like they actually did, those contractions and "gonna"s and "woulda"s and "shoulda"s would signal a kind of sloppy casualness to us today. It would feel anachronistic, even at the moments it was most historically accurate, because we've constructed the past as feeling a certain way, and because, semiotically, what a contraction stylistically communicates has changed.
This problem came up before with Deadwood. If the curing in the show had been historically accurate, if the characters had cursed the way people cursed in the American West in the 1870s and '80s, modern audiences would have laughed. "Gosh darn," and "tarnation" don't carry the weight or the force they did. What they mean, of course, hasn't exactly changed, but the context-constructed emphasis of the words is totally different now. The show chose to try to maintain the right mood using contemporary cursing, figuring that feeling authentic was more important (and achievable) than being lexicographically correct.
Both shows, I think, walk themselves into situations where it's not possible to not be anachronistic.
2. Imaginations of idyllic pasts persist on many levels.
We know the 1950s weren't the white bread, GOP-fantasy land we've been told it was. We know the myth of good, pre-60s America, where there were no abortions or social unrest or tensions, no gay people or pornography or "deviance," where families just loved each other and women were women and men were manly men, where there was no debt or or poverty or despair, just simplicity and honest, American-dream hard work, is a complete and total crock. A vote-getting fantasy.
Yet, still, we imagine they, in those halcyon days, spoke more properly.