Malory's rivalry with their friend Trudy Beekman is a reference to Lucille's rivalry with her neighbor/friend in Arrested Development. The actress plays both characters. Sterling even says, "Wow, you don't get along with your neighbors anywhere."
The visual nod to actor David Rees Snell, whenever Archer is shown with a mustache. Not to mention, the fact that Woodhouse's unrequited love was named Reggie, which is a variation of REG (the initials of Snell's character on The Shield).
Archer's rampage in "Placebo Effect" is, in his own classic style, a (deliberate) Shout-Out to pretty much every Roaring Rampage of Revenge plot in the kind of media Sterling would partake in. For just a few examples, the grenade up the ass is quite similar to scene in Man on Fire, and "Did you see Regis this morning?" is a play on a famous ending from Magnum, P.I..
Cheryl's family, the Tunts, are an expy of the Vanderbilt family, from their railroad fortune down to there being multiple "Corneli-i", to the "Tuntmore" (Biltmore) House and a matriarch who is nostalgic for the days of slavery.
"White Knights" has Archer barefoot for most of the episode. There is a lot of broken glass involved.
"This agency is not your personal bank account for you to jet off to Whore Island!"