"Where did you get a grenade? It was hanging from the lampshade!" "A Hanging Lampshade" is a term writers use when they are explicitly making reference to an implausible story line.
Archer's "I would prefer not to" is a reference to the book Bartleby the Scrivener by Herman Melville, in which the character frequently says this line. In response to the bemused listeners, Archer adds: "Not a big Melville crowd here, huh? He's not an easy read."
Spirodon Skorpio calls Archer "malaka", which is the Greek word for jerk, on two occasions. He also refers to Lana as a "tsoula" and a "poutana", both meaning whore in Greek.
On the plane, when Malory mentions she used to spank Archer with a wooden spoon as a child, and Lana replies, "It sure explains the ping pong paddle", the flight attendant glaring at her is the same one Archer had bedded in Mole Hunt (2009) and, judging from the red imprint on her buttock, spanked with that notorious ping pong paddle.
The magazine that Jakov is reading when he meets Mallory at the airport is the same one Charles and Rudy were reading in Honeypot (2010), and it has an homage to Skytanic (2010) on the back cover.