At the end of every episode, the card for the production company Spitzer Holding Company features a variety of items they specialize in. In this episode they list Non-Erotic Lingerie, Voter Registration and Suppression.
Amy's fake name tag says "Mila".
One of the obstetricians is named Dr. Sidian, thus O.B. Sidian, a play on words ("obsidian"); the other O.B. doctor is played by Orson Bean, apparently a play on his initials.
Cheyenne does not appear in this episode.
The music playing when the two men get their IV drips tangled is a remake of the 1994 song "Kiss From a Rose" by Seal. The music playing while a man in the clinic waiting room is coughing underneath a "cover your cough" sign is a remake of the 1989 song "Everlasting Love" by Howard Jones. Apparently the hospital and clinic both use the same off-brand music service as Cloud 9.