When Cyril is searching how to defend against hypnosis, his screen says "10^100 SEARCH". This is an obvious play to a Google search as the number represented by 10^100 is a 10 followed by 100 zeros, or a Googol. Google founders used this word to name their company because they wanted to show how much information they could retrieve with a single search.
(at around 5 mins) Malory Archer says "Trust me, if there's a Hell, those creepy Dulles brothers are in it, doing unspeakable things with bananas." This is a reference to the fact that in 1954, John Foster Dulles and Allen Dulles led a CIA mission to depose the leader of Guatemala that benefited the company United Fruit.
The show revolves around the CIA's MK Ultra project focused on mind control. One aspect of the project was to create multiple personalities so that agents wouldn't even know they were agents until activated. Christian Slaterappeared in the short-lived My Own Worst Enemy (2008) in which he played a CIA agent with multiple personalities, one of which didn't know he was a spy.
When Cyril starts a computer search on how to defend against hypnosis, the top of his computer screen says "Pirate Virus Ready". This refers to the virus given to Cyril by Spelvin in Tragical History (2011).
When Archer Lana and Slater are turning left onto Sunset, there is a Charlene billboard hidden in the back that matches their tour bus from when she was a country singer.