Viktor St. Clair was a persona Jimmy assumed in the Second Season Premiere, Switch (2016), when he and Kim ran their first confidence game together, on the foul-mouthed stockbroker Ken.
"Escape (The Piña Colada Song)" by Rupert Holmes is playing at Kim and Glenn's cookout. In Nailed (2016), Jimmy and his film crew gain entry to an elementary school by convincing the principal that Holmes was an alumnus of the school.
According to AMC's Talking Saul, Vince Gilligan said that six years have passed from the dissolution of Saul and Kim's marriage to the present day.
The birthday card that Kim signs for her office mate is similar to the office birthday card that Mike is asked to sign when he does a drop-by security inspection at Madrigal in episode 4.1 (Smoke). The birthday cards are both cat themed and use the same pun, "purr-fect," in their punchlines. This is a way of illustrating the mundanity and uniformity of office culture.
Jimmy told Kim to put on a "hairshirt". A Hairshirt is a type of garment made from rough animal hair (usually that of goats) like an undershirt which pressed against the skin so the coarse hair will rub and scratch the wearer. It was especially used by monks in the Middle Ages, a type of mortification for committing a venial sin.