Danny, already starting to get panicked, looks more so when Don confirms that he and Roger did in fact speak, and then Peggy tells him it was really a pleasure to meet him in the tonal equivalent of the music they play at the Oscars when a speech is taking waaaay too long. They stand (oh my God, I forgot how short Danny is; even Peggy is towering over him) and Don wishes him the best of luck, which seems like poor etiquette; Peggy gives him a more standard "We'll let you know" before Danny asks if they know a good place to eat around there. Don, unwilling even to throw him this bone, suggests he ask his secretary on his way out, and after he's left, we hear Miss Blankenship's inimitable voice bark, "I don't work for you!" Heh.
Don asks Peggy if they're on Candid Camera, but I'm guessing from her behavior later in the episode that she doesn't typically worry about such things. Peggy replies that there's no way Danny is twenty-four. "I'm twenty-five!" Heh, cute, although Elisabeth Moss's actual age of twenty-eight is a lot closer to the mark than Danny Strong's thirty-six. After Don explains that Danny is Jane's cousin, Peggy tells Don that it's a relief to see someone worse than she, and given that she's always projected an air of extreme competence, she's obviously fishing for a compliment, which makes Don's amused "Don't get used to it" acceptable in context. Peggy presses on, though, saying that her work has come so far and citing Glo-Coat as an example, but that's not the most positive subject for Don: "You finish something, you find out everyone loves it right around the time it feels like someone else did it." I'm just glad independent film is free of such lengthy timetables.
Not sure how to reply to that, Peggy asks if that's what Don's going to say at the Clios, and when he tells her they don't have speeches, she confidently says they're going to win, and tries to get him to admit he's excited. He does concede that it'd be great for the agency, adding that Grey doubled its value in five years just based on awards, before changing the subject and asking if she's got anything on Vicks. She tells him they're very behind, and relates some horror stories about the new art director, but Don tells her the guy, "Stan Rizzo," is talented and more experienced, so Peggy needs to learn how to work with him, not the other way around. Faced with that recurring disapproval from Don she so hates and yet can't seem to avoid, Peggy wishes him luck that afternoon and exits.