My wife and I just finished watching this. Holy crap. It was amazing. Here's my take as a musician/composer/arranger.
It reminds me in many ways of Once More With Feeling, Buffy The Vampire Slayer's musical masterpiece of an episode (which I now see was just referenced above this post!).
While I'll have to sit with it for a bit before declaring it to be on par with such a classic, I think it might be up there for me.
What Buffy did, and this episode as well, was work major plot points and character development into the songs, to give them weight both at the time and later in retrospect.
I found a fair portion of the songwriting in this episode to be stellar. La'an's solo piece in her room laid bare many of her thematic elements that were shown but not outright stated in her time travel episode.
And Christine's and Spock's contrasting arrangements of the same melody were superlative. They demonstrated musically how two people can be on completely different pages with completely different takes on an identical event by giving them completely different vibes with completely different emotional content through alternate arrangement of the same melody. It essentially went from Mardi Gras to a funeral dirge through nothing but musical arrangement.
Plus, the wordplay. Jesus Christ, the wordplay. The way Spock went from singing about "why...I'm the ex," to "I solved for Y...I'm the X," was just fantastic. He's the independent variable, the predictable one, the reliable one, the one whose every move can be counted on, and he was dealing with a dependent variable - the one capable of moving up, down, and back again while he marches forward steadily.
It was a frickin' algebra metaphor wrapped in a homophone pun and sung during a parallel musical arrangement contrasting their approach to the same melody and event. The number of levels on which that operated had me flipping out. That's some serious top-tier songwriting right there.
In order to temper my gushing, I'll give my biggest criticism. I hate how autotuned everything is now. Like Glee (which I hated), they're autotuning the great singers alongside the crappy ones in order to keep the weak ones from seeming so out of place. La'an and Uhura clearly needed no autotune, their control over their tone, vibrato and the transition from chest voice to head voice showed that they're both technically proficient singers who would have sounded amazing without the added sheen (more so, in my opinion).
But man, that was a fun watch (and listen).