• This episode was directed by Johnathan Frakes, who starred in the ENT episode, “These Are the Voyages...”
• Captain Burnham informs Rayner that the Breen Primarch Tahal is going to be arriving at their location in the next episode. We learned in “Erigah” that Tahal occupied Rayner’s homeworld, Kelerun, and used it as a staging point.
• The tool Book is using to help effect repairs on the spore drive looks to be the same one he used as a weapon against Burnham in their fight when the characters first met in “That Hope Is You, Part 1”.
• The Progenitor’s technology is contained within a structure carefully balanced at the point where the gravity wells of two black holes intersect, i.e. the Lagrange point. Hey, that’s the title of the episode! Which makes sense, because the rest of the episode must surely be about figuring out how to retrieve the structure from such a precarious position without being crushed, torn apart, or spaghettified by the intense gravimetric interactions. It would be silly if, say, the Breen dreadnought was to show up and simply yoink away the structure with a tractor beam while we’re still in the cold open, and the Lagrange point did not matter for the rest of the episode.
• The structure containing the Progenitor technology looks like a large barrel. Somewhere in Sto’vo’kor, a warrior punches a wall and doesn’t understand why.
• Moll stores L’ak’s body in a portable transport buffer. Trek has been using the transport buffer to store people since Scotty did so in “Relics”, though the other engineer aboard the USS Jenolan, Franklin, a good lad, pattern degraded too far for him to also be retrieved. Presumably no one would notice if L’ak’s pattern degraded over time.
• Adira mentions having been part of the Earth Defense Force, which is what they were doing when introduced in “People of Earth”.
• Burnham’s plan for infiltrating the Breen dreadnought is to transport through a gap in the shield coverage near an exhaust port. In “Preemptive Strike”, Ro and a team of Maquis exploited a weak point in the USS Enterprise D’s shields created by the ship’s impulse engines to steal medical supplies.
• Rayner asks Tilly to be his acting first officer while Burnham and Rhys are on the Breen ship. Saru also promoted Tilly to be his acting first officer while she was still an ensign.
• The away team plans to move around the Breen dreadnought in replicated Breen suits. In “Indiscretion”, Kira and Dukat disguised themselves in stolen Breen suits to infiltrate a work camp.
• When Burnham activates her helmet, it forms around her head, but her braids are still visible hanging down her back before the transport. Upon arriving on the Breen ship, Burnham’s braids are no longer exposed. Later, when Burnham deactivates the helmet, her braids are already hanging down her back before it starts to dematerialize.
• Despite being Federation technology, the fake Breen suits still have Breen script in their HUD.
• Burnham uses the term “achworm” during her bluff, something Primark Ruhn called called the Federation representatives in “Erigah” before it became apparent that T’Rina speaks the language.
• Assembled at Federation Headquarters we see:
• Two Eisenberg-class starships
• A Saturn-class starship
• A Merian-class starship
• Two Mars-class starships
• One starship of the same class as the USS Dresselhaus
• One 32nd century Constitution-class starship
• One 32nd century Intrepid-class starship
• T’Rina suggests sending the USS Mitchell to intercept Tahal’s fleet. The Mitchell first appeared in “Rubicon”.
• ”A shuttle wouldn’t be remotely capable of engaging her entire fleet.” President Rillak seems to imply that the Mitchell could conceivably be a match for a Breen fleet, which I would argue is very appropriate for a ship named for Kenneth Mitchell, who played Kol, Kol-Sha, Tenavik, and Aurellio on DIS, and voiced the Tweerk captain, one of Ransom’s Starfleet black ops buddies, and a Romulan guard on LDS before his passing.
• Burnham uses her xenoanthropology specialization to understand that joining a Breen feast day would be considered a good thing to do. Xenoanthropology was established as Burnham’s scientific focus in the series premiere, “The Vulcan Hello”.
• Burnham relates the results of her self introspection in “Labyrinths” to Book.
• ”Grum of osikod,” is a reference to the Kellerun epic, The Ballad of Krul. Burnham quoted the passage in which it’s mentioned to Rayner in “Mirrors”.
• ”Oh, holy schnoodle.” In “Choose Your Pain”, Tilly was the first person to say ”fuck” in Trek.
• Before sitting in the captain’s chair, Rayner does a one handed variation on the Picard maneuver.
He memorably played "unconscious guy on a table" in "Shades of Gray."
A tour de force