Los Angeles Aztecs were a defunct L.A. based soccer team that competed in the North American Soccer League from 1974-81. Archer tells Barry that if he's come to L.A. to see the Aztecs play he's got some bad news for him.
It is revealed that the full name of "Barry Dylan" is "Bartholomew Aloysius Dylan", which means his initials spell "BAD".
The show references the short Electrocuting an Elephant (1903). Topsy (2013) goes further into detail of this short. H. Jon Benjamin is the title role in both series.
Archer makes reference to the 1937 novella "Of Mice and Men" when he says, "quit squeezing the puppy, Lennie" to Lana, as she is bandaging his leg.