The Star Trek Universe bumper features Discovery jumping in with her spore drive then flying off at warp.
If anybody’s questioning whether one can actually survive on the outside of a ship traveling at warp, the answer is yes, as long as they are within the starship’s warp bubble (ENT: “Divergence”, where Trip moved between Enterprise and Columbia while the two ships shared a merged warp bubble). There is a mistake in the closed captioning which says “warp level” instead of “warp bubble”.
Tonic 2161 is named after the year the Federation was founded. Although it’s for the Millenium Celebration, the current year is actually around 3188 (stardates have been a bit wonky ever since DIS went to the 32nd Century), hence the “give or take a few decades” remark. The stars in the cocktail taste like jumja sticks, a sweet Bajoran delicacy made from the sap of the jumja tree (DS9: “In the Hands of the Prophets”).
The holographic nametag for Stamets is not a screen overlay, but comes out of his tricom badge (DIS: “Die Trying”), a 32nd century combined tricorder, comm badge, holographic PADD and personal transporter. The pathway drive was first mentioned back in DIS: “Kobayashi Maru”, where a prototype was installed on the Voyager-J and Burnham was under consideration for being her captain. There were no details on how it worked, however.
Tilly says it’s been “months” since Burnham has talked about Book, which means some time has elapsed since the end of Season 4. There is a brief shot of a Lurian speaking to another alien I’m unable to identify.
T’Rina mentions the Tholian Republic and Breen Imperium. There have been political changes since the TNG era, since back then they were the Tholian Assembly (TOS; “The Tholian Web”) and the Breen Confederacy (DS9: “Strange Bedfellows”). Her relationship with Saru has grown more serious, as evidenced by her use of the word “love”.
800 years - if exact - puts it at 2388, after the Mars Attack (2385), Picard’s resignation from Starfleet (2386) and the Romulan Supernova (2387). This is the first mention of a “Red Directive”.
The dessicated Romulan corpse has the forehead ridges of that mark them as a Northerner (PIC: “The End is the Beginning”).
Burnham’s phaser pistol can transform into a rifle configuration, presumbly by the same method that allows it to be stowed as a device on the sleeve (first seen in DIS: “Terra Firma, Part 1”).
Captain Rayner is a Kellerun (DS9: “Armageddon Game”). We see a tribble in the corridor, perhaps the same one from DIS: “Kobayashi Maru”.
Moll and L’ak stole a tan zhekran, a Romulan puzzle box. We saw an example of it in PIC: “The Impossible Box”, where it was used as a booby trap.
Tilly is of course speaking of her ice moon escapade with a group of cadets on Kokytos in DIS: “All is Possible”. This is the first mention of Andorian champagne (or should that be Andorian sparkling wine?) - previously the only Andorian alcoholic beverage we were aware of is Andorian ale.
Fred is a synth (PIC: “Maps and Legends”), with the same golden skin and eyes as Soong-type androids like Data, and has lived for at least 622.7 years (c. 2565), the last time he saw a Romulan puzzle box. Among the items L’ak and Moll offer is an infamous self-sealing stem bolt (DS9: “Progress”).
The book inside the puzzle box appears to be filled with Romulan writing. Booklice, or Psocoptera, are real in case there was any doubt.
Fred’s internal memory drive has the serial number AS-0572Y. Stamets connects that to Altan Soong, which might mean Fred is from Coppelius (PIC: “Et in Arcadia Ego, Part 2”). Altan was last seen in a holographic recording in PIC: “The Bounty”, having died between 2399 and 2401.
Burnham says she hasn’t hated anyone this much in 930 years, which dates back to 2258, the year Discovery jumped to the 32nd Century.
Tilly says the database is using 256 qubit (captioned as “Q-bit”) shifting fractal encryption. Breaking into is a violation Security Protocol Six Alpha.
Discovery jumps back in at Archer Spacedock, installed around Federation HQ and first unveiled in DIS: “Kobayashi Maru”.
Let’s hope that Saru and T’Rina’s wedding isn’t as violent as Spock’s (TOS; “Amok Time”). Stamets says that they were about to download 15 teraquads of data from Fred’s eye. A quad is a fictional unit of data invented for TNG, deliberately kept vague to avoid comparisons to today’s bytes. 15 teraquads sounds impressive, but in VOY: “Drone” the advanced Borg drone One was said to have assimilated 47 billion teraquads.
Kovich shows Burnham that Dr Vellek was there on Vilmor II at the climax of TNG: “The Chase”, where Picard discovered that many species of humanoid life in the Galaxy had been seeded by a precusor race, the Progenitors.