Una mentions that "Ad Astra Per Aspera" was the motto of Starfleet before the founding of the Federation. The insignia for Starfleet Command, on both arm patches and flags, on Star Trek: Enterprise (2001) consisted of a yellow arrowhead on a blue round star background, which was framed by a thick gray inner border and a thin red outer border. Inside the gray border, there were more white stars and the Latin words "Ad Astra Per Aspera".
Just before her trial begins, Una is warned that not taking a plea deal would result in a minimum sentence of at least two years in a Starfleet penal colony. This was established in the DS9 episode Doctor Bashir, I Presume (1997), where Julian Bashir's father received this sentence when he took full responsibility for Julian's genetically engineered background, and his subsequent joining of Starfleet as a doctor.
La'an states in her testimony that she has been promoted each year of service to Starfleet. As she only holds the rank of lieutenant, that would mean she has only been in Starfleet for 2 years, enough time to go from an ensign to a lieutenant junior grade to a full lieutenant.
This episode's title (Ad Astra Per Aspera) is the state motto for Kansas.
The literal translation is "to the stars by rough(ness)." Starfleet actually uses the translation "To the stars by difficulties" but "Toward the stars by adversity" is a better translation.