David says sarcastically to Maddie, "Yeah, you're a regular Jan Murray." Jan Murray (1916-2006) was a Borscht Belt comedian in the 1930s who moved on to perform at Las Vegas venues in the 40s, host game shows in the 50s and 60s, and appear regularly on TV as a panelist and guest star in the 60s through the 80s.
David suggests that Maddie's sheepdog had been "looking for a zipless tick," referencing the "zipless f*ck" (or sexual encounter unencumbered by emotional entanglement) sought by the heroine of Erica Jong's popular novel Fear of Flying (1973).
The title references "My Fair Lady," the Lerner and Loewe musical based on Pygmalion by George Bernard Shaw and first appearing on Broadway in 1956 and adapted for film in 1964. The plot concerns a poor Cockney flower seller being trained to speak proper English and be presented as a sophisticated well-bred lady to high society on a bet between two upper class and arrogant men.