Ransom fights exclusively using a two-handed punching style. Fight choreography in older Star Trek shows was somewhat infamous for its poor quality and featuring an unrealistic fighting style comprised mainly of two-handed punches.
Giving a longer time for an engineering repair or project than it will actually take, as well as impressing others by finishing sooner, was a tactic used by Scotty on the original Star Trek. He explained it to Geordi LaForge when he guested on STNG.
While in the turbolift before Captain Freeman enters, Boimler is humming the theme from Star Trek The Next Generation.
Great Bird of the Galaxy was a nickname for Star Trek creator Gene Roddenberry.
Mariner states that the away team lives on a spaceship and therefor no one will be dying of a spear wound. A replica of Abraham Lincoln was infamously killed by a spear wound in the original series episode "The Savage Curtain."