The “half” refers to Spock, who is only half-Vulcan.

The Stardate is 3111.1, and Enterprise is headed for Purmantee III where the crew will take shore leave. Una says La’An, of all people would understand why she’s remaining on board, as she likes to do work when it’s quiet. Indeed, the two did that in SNW: “Spock Amok” when the crew was on shore leave in Starbase 1. This is the first mention of Greerian cocktails.

Vice-Admiral Pasalk is a Vulcan who headed the JAG office in SNW: “Ad Astra Per Aspera”. He also has an antagonistic relationship with Spock, although that is only apparent to people who can read Vulcan body language, like M’Benga. Batel was a JAG officer who was then promoted to command, being recalled to JAG duty for Una’s trial in that episode.

Tezaar is an M-class planet (Minshara-class, as per ENT: “Strange New World”), capable of supporting humanoid life, but are not warp capable, hence protected by the Prime Directive. Spock explains that the Vulcans made contact with Tezaar before the founding of the Federation (in 2161), but we know that Vulcans had their own non-interference directives long before before official First Contact with Earth in 2063 (see ENT: “Carbon Creek”), as La’An points out.

Spock was turned human and back again by the Kerkhovians in SNW: “Charades”. Pike being overwhelmed by emotions is an expected response, as Vulcans feel emotions much more intensely than humans, hence the necessity to practice arie’mnu (passion’s mastery) to control them. However, given this is a learned response, the sudden snap to “emotionless” Vulcans requires some explanation.

The song is “Reckless Youth” by indie group The Home of Happy. Pike is carrying a lirpa, a traditional Vulcan weapon first seen in TOS: “Amok Time”. Ortegas mentioned she had fought with a lirpa in “Spock Amok”. The away team also carries cylindrical hardshell duffle bags, which were first seen in TNG. Music reminiscent of the Vulcan fight music of “Amok Time” can also be heard as part of the soundtrack.

Pike’s opening narration for this episode is in a stilted manner, as a nod to his status as a Vulcan.

Una’s explanation for why the away team is acting so coldly is because the serum was derived from Spock’s “perceived experiences”, leading them to assume the manners that Vulcans normally years to develop. That being said, how a serum can be based on “experiences” is not explained.

Kirk’s mention of Sam reminds me that we haven’t seen him since SNW: “Wedding Bell Blues”.

It is well established that Vulcans have an enhanced sense of smell compared to humans and that they find human odors unpleasant. As mentioned in ENT: “The Andorian Incident” and “Spock Amok”, Vulcans take nasal suppressants/numbing agents to help with this.

La’An’s obsession towards martial matters and conquest is meant to seem Romulan in nature (as Kirk says, aggressive and manipulative) but as we find out later, it’s her Augment ancestry influencing her Vulcan state.

It’s interesting that M’Benga and Spock are now talking openly about katras, when it was first presented as a deeply personal thing to Vulcans (Sarek says in ST III that Spock would not have spoken of it openly). But then again mind melds were also supposed to be things Vulcans didn’t talk about (TOS: “Dagger of the Mind”).

Pike’s allusion to a mission he is not permitted to discuss is his knowledge of the Romulans gained on a trip into an alternate future (SNW: “A Quality of Mercy”). La’An learned about Romulans while also time traveling in SNW: “Tomorrow and Tomorrow and Tomorrow”.

Kintsugi is the Japanese art of mending broken ceramics by filling in the gaps between shards with a metallic lacquer made from gold or sometimes silver. The philosophy behind the practice is to embrace imperfections and find beauty in them instead of keeping them hidden.

15 years puts the end of Una and Doug’s romance in 2244, a year before Enterprise was launched. My best guesses put Una at around 42 years of age (I’ll spare you the math) so she last broke up with Doug when she was 27.

Batel says Pasalk used to call Pike “the human with inappropriate hair”, which is clearly a meta joke as Pike’s hair is a frequent topic of conversation among fans.

Doug attributes Spock’s ability to lie to his human heritage and claims that as a full-blooded Vulcan he cannot lie, but full-blooded Vulcans have been known to lie (or at least obfuscate) before - especially T’Pol and Tuvok - on numerous occasions.

Kirk says he’s served under Vulcans. The current CO of Farragut is V’Rel, a Vulcan female captain.

Plomeek soup is a traditional Vulcan dish, which can be bland or spicy. Chapel made plomeek soup for Spock in “Amok Time”, although Spock, in the throes of pon farr, threw the bowl into the corridor.

It appears that we are meant to believe that it was Kirk who introduced Scotty to the pleasures of Scotch.

Of note in the post-credits scene is that the inability to use contractions was part of the character of Data in TNG (yes, it’s debatable). Also, while his smiles are often wry and subtle, Spock has grinned a number of times before, in TOS: “The Cage”, TOS: “Amok Time” and laughed in SNW: “Children of the Comet” and SNW: “Those Old Scientists”.