The "trial" set up is a nod to Star Trek VI: The Undiscovered Country (1991) where Captain Kirk and Dr. McCoy are framed for murder and are brought to a similar trial setting (except it's a Klingon court). In addition, the aggressive manner in which Clar questions the lower decks officers under duress is similar to how Kirk and McCoy were questioned by Chang (played by Christopher Plummer) in ST VI.
Boimler's suggestion to use the impulse drive to perform a "Crazy Ivan" is a nod to Tom Clancy's The Hunt for Red October (1990). A Crazy Ivan is when a Russian submarine suddenly turns to clear their baffles (the area just behind the propellers), as that is a submarine's blind spot when it comes to sonar.
At one point, Mariner is complaining that on Earth all there is to do is drink wine in a vineyard and eat soul food. In Star Trek: The Next Generation, Picard goes back home to France and his family's vineyard. In Star Trek: Deep Space Nine, Sisko goes back to Earth and eats Jambalaya in his family's restaurant in New Orleans.
The manager of the event silo states that Clar only booked the space for 22 minutes. 22 minutes is the length of a standard episode of a sitcom, minus commercials and credits.
Kurtwood Smith (Clar) is a veteran of three other "Star Trek" projects. He played the Federation President in Star Trek VI: The Undiscovered Country (1991), Thrax in Things Past (1996) and Annorax in Year of Hell (1997) and Year of Hell, Part II (1997).