Commander Garrett Is either the grandmother or great-grandmother of Capt. Rachel Garrett who Is the captain of the USS Enterprise NCC 1701-C In the Star Trek TNG episode Yesterday's Enterprise.
The "Tucker Memorial Medal of Honor" awarded to Commander Garret is a reference to Charles "Trip" Tucker from Star Trek: Enterprise
While in the shuttlecraft, Sulu tells of his "great, great, great, great, great, great, grandfather who grew up in an internment camp during Earth's Second World War." This is a nod to the real life experience of original Sulu actor George Takei.
During the promotion hearing, Mr. Spock states he has been with Starfleet for 19 years, 5 months, 20 days.
The Tellarite Ambassador quotes William Shakespeare's A Winter's Tale in this episode with "A lady's 'verily' is as potent as a lord's"