• Burnham records the stardate as 866274.3 in her personal log.
• Burnham has the recording of the projection of the Progenitor from “The Chase” displayed in her quarters.
• As with season four, it appears that aliens serving Starfleet, specifically the ones whom you would except to have hands notably different from a human’s based on their facial features, wear gloves. Apparently this mandate extends to the admiralty, as we see the Deakohn admiral here covering the shameful monstrosities we can only assume his digits to be.
• In addition to the USS Discovery A and the USS Antares, congregating around Federation Headquarters at various points we see:
• Three Eisenberg-class starships
• Two Courage-class starships
• Two Constitution-class starships
• Two Merian-class starship
• Three Friendship-class starship
• A Saturn-class starship
• A Mars-class starship
• It’s grudge! From Star Trek!
• We learn that Lyrek is a burial world that was used by the Promellians prior to their extinction. Promellians first appeared in “Booby Trap”.
• ”The last recorded exploration was over a century before Doctor Vellek was even born.” That does potentially raise the question of how Burnham would have been so familiar with Lyrek in the previous episode, though of course she and most of the rest of the Discovery crew might have been alive before Doctor Vellek’s birth.
• Saru reveals that it was Jett Reno who gave him the nickname ”Action Saru,” which only makes the fact that we’ve yet to see Reno this season all the more galling.
• ”I remember the day you came aboard Discovery. A mutineer. A prisoner. You seemed exactly the wrong choice.” Saru seems to be overlooking the fact that he knew Burnham prior to her mutiny and imprisonment, as seen in the series premiere, “The Vulcan Hello”.
• Saru implies to Burnham that she should consider making Book the new first officer on Discovery. Book is not a part of Starfleet or any other similar hierarchical organization. Presumably Saru makes the suggestion so that his own choice of ensign Tilly as his first officer in “Unification III” is no longer the wildest choice of in the history of Starfleet.
• Presumably Book could be given field commission, as Chakotay was in “The Caretaker”.
• Adira laments being separated from their boyfriend, Gray who almost immediately booked it off Discovery in “But to Connect…” after his consciousness was transferred out of the Tal symbiont and into a synth gollum in “Choose to Live”.
• On Lyrek, Burnham and Saru encounter parts of statues, including heads that have features similar to the Promellian captain whose log was seen in “Booby Trap”, but the statues have four eyes whereas Promellians only have two.
• The Promellian statues launch flying drones that set to attacking Burnham and Saru. The crew of the USS Enterprise D were also attacked in a jungle by the flying drones of a dead civilization in “The Arsenal of Freedom”.
• ”Tilly, we’re losing our foot!” Burnham is referring to a bit of shelter she and Saru have taken cover under. Nog lost an actual food in “The Siege of AR-558”.
• Lang-cycle fusion engines were established as being a feature of Promellian battle cruisers in “Booby Trap”.
• It was established in “Si Vis Pacem, Para Bellum” that Kelpiens are stronger, and faster than humans.
• We’ve previously seen Saru’s quills stab into a wall, or incapacitate a human, but this is the first time we’ve seem them projected with enough force to obliterate a machine.
• The fact that Kelpien visual acuity allows them to see things outside the range available to humans was seen in “Brother”.
• Burnham and Saru both recognise a type of Romulan poem called a revlav. Burnham and Saru also both come from a time in Starfleet’s history when the Romulans were known to the Federation only as a mysterious enemy.
• ”Diary’s Romulan; Federation’s got no claim to it.” it was established in “Unification III” that the Romulans had reunified with the Vulcans at some point during the in the past, and in “All Is Possible” Ni’Var rejoined the Federation.
• Romulan homes having a false front door was established in “The End is the Beginning”.
• Zora uses programmable matter to create a physical copy the symbol from Doctor Vellek’s diary. This physical version is the one seen in the opening sequence this season.
• Book explained that he got his name from his mentor, the previous Cleveland Booker, in “Species Ten-C”, who was also apparently Moll’s father.
• ”Which, I suppose, makes her the closest thing to family I’ve got left.” Book’s Kwejian family was killed in “Kobayashi Maru”.
• Saru’s pruning knife was a gift from his sister in “The Brightest Star”.
• Saru recounts his experience going through Keplein puberty, vahar’ai, in “An Obal for Charon”.
• Saru told Tilly to avoid touching the swampkelp while it was in bloom in “Choose to Live”.
We've seen that in her one year as a courier, Burnham learned everything about every planet because of secret criminal space knowledge. Even if the last recorded exploration was that old, presumably space pirates with their gritty streetsmart know-how have some sort of Mos Eisley medieval market nearby.