Among the items of contraband Mariner reveals is the infamous Spock "space helmet" toy from the 1970s.
Mariner threatens to feed Boimler to an Armus. This refers to the creature that killed Tasha Yar in Skin of Evil (1988).
Ensign Peanut Hamper is an exocomp, a sentient artificial lifeform first seen in The Quality of Life (1992).
Boimler's choice of a sword as a weapon in the hallway fight is a nod to Lt. Sulu running amok on the original Enterprise with a rapier in The Naked Time (1966)