Commander Ransom demonstrates how to sit in a chair in a "commanding" manner, by throwing one leg over the back of the chair. This was how Commander Riker sat in Star Trek: The Next Generation (1987). The manner in which he sat down was so unusual that fans of the series have taken to calling it "The Riker Maneuver." Various explanations for the maneuver have been offered throughout the years since TNG aired, from Riker actor Jonathan Frakes's well documented back problems, to it being an acting choice to make Riker seem more like "a cowboy."
"The Stars at Night" is a line from the popular song of the 1940s, "Deep in the Heart of Texas".
Rutherford tells the AI "You better stop attacking or you're dunsel." This is a reference to The Ultimate Computer (1968), which was also about replacing crewed ships with AI-run ships, in which Kirk is referred to as "Captain Dunsel", and Spock explains that "dunsel" is a slang term for a useless item.
Captain Freeman orders maximum warp, and a moment later Boimler announces that they're holding at warp 8, confirming that the California-class has a maximum cruising speed of just warp 8. That's incredibly slow compared to its contemporaries, such as the Galaxy-class (warp 9.6), Intrepid-class (9.975) and Sovereign-class (warp 9.995).
The three Texas-class ships that Buenamigo commissioned are USS Aledo (NA-01), USS Dallas (NA-02), and the USS Corpus Christi (NA-03). In US history, when the US Navy wanted to name one of their nuclear submarines "USS Corpus Christi", Catholic politicians protested, saying that a warship couldn't have a name that translated as "body of Christ". So the US Navy appended the prefix "City of", so that the submarine is named after the *city*, not the body of Christ. It has since been named "USS City of Corpus Christi". However, a WWII warship was named USS Corpus Christi (PF-44, a Tacoma-class patrol frigate), and a helicopter repair ship was named USS Corpus Christi Bay (T-ARVH-1) in the 1960-70s.