- U.S.S. Franklin - This century-old starship Kirk and company bring back into working order to stop Krall's plans to destroy the starbase Yorktown (we'll get back to that) is taken from the early Starfleet era depicted in Star Trek: Enterprise, which features the first ship to be called the Enterprise, an experimental design that's the first to hit warp 5. The Franklin is said to be the first ship to hit Warp 4. It's reasonable to assume that it was a design Starfleet worked on in the run-up to the NX-01 (Enterprise), and was later added to the expanding fleet (as the NX-326, if I remember the placard correctly).
- M.A.C.O.s - Its captain, who is introduced as Krall but later turns out to be commanding officer of the Franklin, was previously a M.A.C.O., an army service that helped feed the ranks of the emerging Starfleet program (Enterprise's Malcolm Reed came from a similar background). M.A.C.O.s were featured in Enterprise's third season, which featured the Xindi conflict referenced in Beyond.
- Xindi & Romulan conflicts - Speaking of the Xindi conflict, Elba's character also talks about a Romulan conflict. He's not talking about the events of 2009's Star Trek, which featured the rogue Romulan named Nero, but rather the Romulan War, which took place soon after the events of Enterprise and were the last time in the original canon anyone had contact with Romulans until the original series episode "Balance of Terror."
- Starbase Yorktown - The starbase Yorktown is named in honor of Gene Roddenberry's name for the startship in his first vision of Star Trek. This draft came even before the abandoned pilot "The Cage," which was later incorporated into the two-part "The Menagerie;" the original vision, featuring the Yorktown, had as its captain Robert April, who was later featured in the Animated Series episode "The Counter-Clock Incident," the last episode of the series, in fact.
- The Yorktown is actually takes the design of the original vision for the space station featured in Star Trek: Deep Space Nine.
- Three years into the mission - It might be said that Beyond is a metaphor of the fate of the original TV series, with events coming to a head and seeming conclusion three years into a five-year mission, with the crew forced to justify its ideals in the face of an implacable foe (previously, merely cancellation). Kirk references the episodic nature of his experiences, which is a nod to the series, which is often described as episodic in nature, one mission distinct from the next, which is to say unrelated.
- Cultural differences - The beginning of the movie features a humorous sequence in which Kirk attempts to make peace between two worlds, which proves difficult when a symbolic gesture from one world means something else entirely in the next. Archer faced blunders of this kind in Enterprise ("A Night in Sickbay") during the formative years of Starfleet.
- Death of Ambassador Spock - Those seeing their first Star Trek movie with Beyond may not be aware of the significance of the birth and death years depicted in the movie, assuming he had a fairly short life. On the contrary, Spock is observing the death of his counterpart from the original timeline, where they share a birth year, but Ambassador Spock lived on to the time of Picard (his journey in pursuit of Nero as depicted in Star Trek takes place after Nemesis), and his death picks up where he emerged in his own past. His death is a nod to actor Leonard Nimoy's death in the real world.
- Absent friends - At the end of the movie, Kirk proposes a toast to his crew. As he references absent friends, the camera focuses on Chekov. This is a nod to the recent death of the actor who portrayed in these films, Anton Yelchin, which is referenced in the credits with the "For Anton" card.
Now, some throwbacks to prior movies:
- The destruction of the Enterprise - This is something that happened twice previously, in Star Trek III: The Search for Spock and Star Trek Generations. The saucer separation happens in both Generations and Beyond.
- Abandoning ship - The ship is abandoned in Search for Spock, although it's a limited crew complement (just the main characters, due to unique circumstances), and everyone beams safely away. The crew also abandons ship in Star Trek: First Contact, in a similar fashion to how it's depicted in Beyond.
- Getting an unlocking sequence accomplished - Speaking of First Contact, the way Kirk desperately must unlock a series of panels as he struggles against Krall in Beyond is similar to a sequence in which Picard and Worf desperately work to detach the deflector beacon and thus deprive the Borg of their main weapon in First Contact.
- Rogue villain taking on the whole Federation - This may seem somewhat unique to the terrorism era we're living in, but it's something Star Trek has been doing since at least Search for Spock, in which a rogue Klingon warrior attempts to lay claim to the Genesis Device (it might be argued that Khan is similarly engaged in Star Trek II: The Wrath of Khan, but he's pretty singularly focused on Kirk as a target). Anyway, all four of the Picard movies (Generations, First Contact, Insurrection, and Nemesis) feature what at the time looked almost like Bond villains (Tom Hardy's Shinzon in Nemesis even unmistakably evokes recurring Bond foe Blofeld, last appearing in 2015's Spectre and portrayed by Christoph Waltz), feature this type of villain. Nero fits this model perfectly, and might be the easiest example to spot, and he's probably best understood in that light, the one we're unfortunately experiencing with alarming frequency these days. I'm told anarchists, a century ago, used to use dynamite like this, for what it's worth.
- The passage of time - Kirk deals with this in Wrath of Khan and its predecessor, Star Trek: The Motion Picture, although circumstances have changed considerably. In the original universe, it's because Kirk is literally aging. In this one, it's because he's now older than his father (George Kirk, depicted in Star Trek) was at the time of his heroic death.
- Spock considers leaving Starfleet - Not only is this a nod to the events of Star Trek and their lingering effects, but it evokes Leonard Nimoy's repeated intentions to distance himself from the franchise, both in the aborted second live-action TV series (which later gave way to The Motion Picture, where Spock does appear) but Wrath of Khan as well (Spock's death originally conceived as a way for Nimoy to gracefully exit; he returns promptly in Search for Spock).
This one's for the Star Trek vs. Star Wars fans:
- For as long as these franchises have existed alongside each other, the debate has been constant. And while the Star Trek movies have often tried to ramp up the action Star Wars helped bring to sci-fi movies, the 2009 reboot and its increased budget made the distinction harder than ever to distinguish. I think Beyond makes a pretty clear statement, in contrast to the recent Star Wars - Episode VII: The Force Awakens, in the similar characters of Jaylah (Beyond) and Rey (Force Awakens). Both are living in the ruins of an old ship. One of those ships becomes crucial to the rest of the movie (Jaylah's, which is the Franklin), whereas the other is quickly replaced by a more familiar, albeit well-loved, relic (the Millennium Falcon). Who Jaylah is and how she helps resolve matters is accomplished in one film, while Rey's journey will likely continue for another two films (a Star Wars custom). Where Star Wars handles the fate of empires, Star Trek is keenly concerned with the fate of ideals. (Clearly, they both value the merits of friendship and heroic commitment.)