The whole episode dealt with power (a frequent theme). Peggy is again being felt slighted by Don, who ignores her contributions to the ad that wins a Cleo. At the start of the episode, she is an "equal" of sorts, being in a meeting to hire a new creative guy. He is a nebbish no-talent that got an interview because he is Jane's cousin. Both her and Don reject him and Don laughs about it to Roger, calling it a nice joke he pulled.
The whole award storyline coincides with it being emmy award time. (all the actors got shut out even though the show won again) Don is high after winning a Cleo, and this again leads him to make unfortunate decisions. He picks up multiple women and forgets whom he is with, and pitches a client while drunk. He uses a tagline that the nebbish guy floated, which he forgets while drunk, leading him to be forced to hire him.
This story is similar to a rare flashback where we see how Don got his foot in the door. It mirrors the nebbish guy as Don basically kissed Roger's butt and took advantage of him being drunk to get a job. The difference between them is that Don scheemed the job from Roger by taking advantage of Roger's drunkeness, where Jane's nephew got the job by chance. Roger wanted credit for "finding Don", but we see he did no such thing, he brushed Don off repeatedly and Don only got the job because Don told him he hired him, and Roger couldn't contradict it.
Back in the day, Roger was the world beater and we learn he was "roaming" Joan's hillsides for a long time. The question is left open as to whether Don just did the same thing.
Peggy and Pete both assert themselves over their adversaries too. Peggy collars the new art guy by going au natural and calling his hedonistic bluff in the funniest story of the episode, while Pete lords over Ken with his partner status. Great line by Ken saying "I can see nothing has changed". Although Pete is portrayed as more competent this season, he still is the same guy.
Great scene that ties into the theme is both Don and Roger holding Joan's hands before the winner is anounced. A real passing the torch moment. Joan seems to be tired of Roger, which will crush the people hoping for a Roger/Joan love match. Roger is doing his memoirs (which are delibertly portrayed as boring) and the whole season is dealing with his being put out to pasture.
Pete, Lane and Don are the firm and Lane basically tells Pete Roger is old news. Pete is accounts and he needs young hungry people like Ken to help with the load. It was the most stark scene yet that Cooper and Sterling are being put to pasture. Don is Sterling when he started and Pete and Peggy are the future, with the caveat that nebby guy may rise past Peggy in the male dominated world of the 60's.
Finally, Don is again out of control, picking up girls he doesn't even know their names (thank god for nametags) and is forced to hire a guy he despised (like Roger with Don) because of his alcohol abuse. He hit on the researcher, who rejected him, but her touching and straightening his tie shows us she is interested, just not when he is drunk. Good money is still on her prediction for Don is true, he will be married, to her.