The actor Chris Doohan, who plays Lt. Montgomery Scott "Scotty" in "Star Trek Continues," is the son of James Doohan who played Scotty in the original series.
The Character Dr. Elise McKenna is named after a fictional 19th century actress from the book "Bid Time Return" written by Richard Matheson. Matheson also wrote the screenplay for "Somewhere in Time" which is based on his book "Bid Time Return".
Vic Migongna, Todd Haberkorn, and Chuck Huber have worked together in the past on projects such as "Soul Eater" (2008) as Death Scythe, Death the Kid, and Franken Stein respectively and "Fullmetal Alchemist: Brotherhood" (2011) as Edward Elric, Ling Yao, and Shou Tucker respectively.
As mentioned in the Storyline, Star Trek The Original series (TOS) was supposed to be on a Five Year Mission, but NBC canceled it prematurely. Star Trek Continues (STC) picks up where TOS left off, finishing the Five Year Mission with 11 final episodes, many picking up from TOS episodes.
The Enterprise Computer is voiced by Marina Sirtis, who played Deanna Troi in Star Trek Next Generation. That character's mother was played by Gene Roddenberry's wife Majel Barrett - who did the voice for TOS Enterprise Computer.
The first episode, "Pilgrim Of Eternity", picks up 2 years after TOS episode "Who Mourns For Adonais" when the God character Apollo reappears, but much older. The reason he appears much older is that he's played by the same actor from nearly 50years before, Michael Forest.
The third episode "Fairest Of Them All" follows on from TOS episode "Mirror Mirror" with a piratical Enterprise in a parallel universe. That universe's Enterprise computer is voiced by Michael Dorn, who played Worf in Star Trek Next Generation.
Credits at the end of the episode "Fairest of Them All" confirm shuttlecraft scenes were filmed at Nasa's Space Center in Houston, where they house the real original full-size Galileo from the original series, built in 1966 by Gene Winfield, and restored by Adam and Leslie Schneider in 2013.