This observation reminds me of another underrated Glee thing. Good musicals make performances an extension or advancement of a plot element that has been established in dialog earlier ("plot to song"). While Glee also has random numbers which are not at all or at least only loosely related to plot (e.g. practically all Warblers numbers), the show does this pretty often. However, Glee also does something that is rather untypical for musicals, that is making a performance the actual origin of a plot evolvement because of the strong emotional reactions the performers or their audiences show ("song to plot"). Examples include practically all instances when Rachel falls for a guy, e.g. for Finn during "You're the One That I Want" and for Will during "Endless Love" (no build-up in both cases) or for Jesse during "Hello" and for Blaine during "Don't You Want Me" (only minimal build-up in both cases).
As far as "song to plot" instances go, Puck's "Sweet Caroline" in "Mash-Up" is the most significant number Glee has ever done. Just look at the reactions of no less than four people in the audience: Rachel acknowledges that Puck might be a suitable mate for her after all; Finn is jealous, although he has no right to be so, because he's with Quinn at the time; Quinn shows a reaction similar to Rachel's, making this the origin of the idea to give Puck a try-out as her child's father three episodes later (which, because of Puck's simultaneous "sexting" with Santana, in turn leads to the Quinn-Santana rivalry which becomes so prominent in the first episode of season 2); and Santana shows a reaction similar to Finn's, making this the point of origin of her sexual rivalry with Rachel, which, although the object of jealousy later shifts from Puck to Finn, has its strongest repercussion with the Finchel break-up in "Special Education." (And btw, "Sweet Caroline" also has one of those beautiful Mike-Brittany moments
Wonderful observations, especially the insight you provide on "Sweet Caroline"! Just like you mention the correlation between song and plot, I'm going to say that we often neglect to appreciate the correlation between song and character development. I really enjoy how many of the musical numbers aren't just filler, but play active roles in furthering a character's understanding of herself and also highlighting less obvious struggles or feelings to the viewer.
This is especially true of Rachel because of 1) her status as a three-dimensional character decides that her tangle of thoughts and feelings are invariably more complicated, and 2) the the show's narrative construst: we're asked to empathize with her, the outsider, time and time again (by being shown how she truly works through her solos) when none of the other characters will, sometimes not even Finn. For instance..."What I Did for Love"
Because of Finn's line "you didn't do this because you love Glee club, but because you love yourself more," a lot of people may have assumed that Rachel's extremely selfish act of sending Sunshine away was done out of her love for herself. While this is partly true, it is also equally misleading. Rachel's "love" for herself isn't rooted in vanity as much as it is in her self-preservation instincts, which inevitably kick in whenever she doesn't have anything to hang on to. But really, the whole aim of her character is to be embraced by the Glee club, to be welcomed into the circle by her friends--former friends, sorry. Everything about the way it's shot, with a lonely Rachel walking the halls by herself, and especially the cut to an isolated Rachel standing outside of the Glee club looking in (very subtle, as usual
), is enough evidence of this. In other words: the solo allowed us to see that the real
reason behind her disastrous decision stemmed from her desperate attempts to cling onto the love and acceptance she received recently from her peers, love and acceptance she didn't get last year from Shelby, from Jesse (and ended ironically in a reverse order as she had planned). "Firework"
Here, Rachel takes Finn's "fireworks" comment, a perceived diss to their relationship, and turns it around, against him--for her. You want fireworks, huh? I'll show you a firework.
She channels her pain and converts it into new energy, doing exactly what Kurchelcedes were talking about during the sleepover. And in this way, this pivotal scene is not just an unmoving tableau that "captures" Rachel's mood-of-the-moment, but her internal crossing in motion: self-awareness reached through the purging of emotion, reached by "singing about it." Lea does a fantastic job at working the transition point when she suddenly breaks into that 1000-watt grin midway through the song.
Aside from the implications it has for her character development, Rachel's pursuit of "Firework," which is bursting to the brim with authentic passion and meaning, also serves to further cheapen the so-called "fireworks," the petty game, that Finn is intent on pursuing.