When Mariner is talking in her sleep she mentions "...buried alive," "...marooned for all eternity" and "...moons of Nibia," all of which were snippets of Khan's speech to Kirk in Star Trek II: The Wrath of Khan (1982).
Boimler is nearly seduced into jamaharon by an Anabaj. Mariner later suggests that her Ferengi friend Quimp try jamaharon with his wife during their planned visit to the pleasure planet Risa. Jamaharon is an undefined ritual, strongly implied to be of a sexual nature, mentioned throughout the Star Trek spin-offs that take place in the 24th century. As is the case here, it is never explicitly explained what the ritual actually is.
Ensign Tendi wonders why General K'Orin's name sounds familiar. Mariner mentions that all Klingon names sound similar, and that they all have apostrophes for some reason. Tendi exclaims, "Yes!" Tendi's first name, D'Vana, has an apostrophe.
The bridge simulator that Ransom puts Rutherford through says that the ship's kindergarten was wiped out by an asteroid. No children have ever been seen onboard the Cerritos. It is unclear if there are families aboard the Cerritos and they are simply never seen, or if the kindergarten class was included in the simulation to increase dramatic tension.