Show creator Matt Weiner told Vanity Fair magazine that the "chip and dip" tray wedding present that Pete returns had been a wedding gift to Weiner's parents.
When the men in the office are having the Nixon vs Kennedy debate, they mention the woman Nixon 'slaughtered' in California. They don't name her, but they are referring to Helen Gahagan Douglas. Nixon beat her by implying, falsely, that she was a communist - he picked up on a derogatory nickname her "The Pink Lady" (saying she was "pink right down to underwear") and she, in return, was the first to call him "Tricky Dick."
"Chip 'n Dip" is said six times in this episode, five of those times are within the first 23 minutes. "We got two" is said four times.
To further on the "Pink Lady" line by Roger referring to Nixon: Richard Nixon himself never called Helen Gahagan Douglas "The Pink Lady"... that is, he didn't make it up. It was Manchester Boddy, owner and publisher of the Los Angeles Daily News, who called her that. Nixon simply referred to Boddy's already declared and published statement.
Obviously Allison Brie couldn't appear in this episode, and they only use her voice, chewing out Pete about the tray.