If you look on the book shelf in Mayweather's quarters aboard the Horizon, there is a white book entitled "Gangsters of the 20th Century," suggesting that this is the same ship Horizon that played a major role in the backstory of A Piece of the Action (1968).
The tables in the Horizon's mess hall are actually from the USS Voyager's mess.
Mayweather mentions to Reed that Starfleet should post families together on their star ships followed by Reed rebutting that they better post a psychologist to deal with the stress. This is, likely, a reference to Enterprise D from Star Trek: The Next Generation (1987) on which many families are posted together along with Counselor Deana Troi.
In Mayweather's old room on the Horizon, a model of Zefram Cochrane's vessel the Phoenix can be seen in the background.
This episode marks the second instance of T'Pol breaking the Vulcan taboo against touching food with one's hands as she eats popcorn during movie night.