The meaning behind the titles. Progressive is made by the original team behind Classic and implies that it has a connection to Classic as a sequel (ex. progressing forward). Alternative takes place from a completely different perspective in both the creative team and cast, like if Classic was made today.
Progressive Rock is also known as classical rock, again fitting with how Progressive is presumably a more direct sequel to the original series than Alternative, which is somewhat ambiguous as to its status regarding whether or not it's a prequel or a sequel (Word of God is that it was initially intended to be a prequel, though various indicators such as the tech and Haruko's more mature and wizened characterization— at least by her standards— imply that it could also be a more distant sequel).
With revelations in episode 4 of Progressive, Canti's strange demon-headed absorption of Naota in the original series was retroactively given a reason (which makes sense in hindsight): it was the effect of acting as a medium for Atomsk from his imprisonment, which is matched by when Haruko absorbs Jinyu back into herself in an identical fashion thanks to having Atomsk power.
This also adds a potential, retroactive Pet the Dog for Atomsk: whereas Haruko reabsorbing Jinyu is done violently and permanently without a hint of mercy, Canti's absorption of Naota was never permanent and he let the kid loose, even when he managed to harness Atomsk's power.
In episode 4, Haruha's age is listed as 16, despite the fact that the series takes place eighteen years after the original series. Outside of the obvious reason, there's another possible reason for this: it may have been sixteen years since Haruko gained the power of Atomsk, only to be split into Haruha and Jinyu.
An interesting one regarding Hidomi Hibajiri that may cross over into Fridge Horror. In the very first episode, Haruko shows Hidomi extreme hardcore porn. Hidomi doesn't so much as react; she neither becomes flustered nor visibly turned on. At first, this seems to be an extension of her emotionless girl/tsundere persona, but as the show goes on, it actually becomes clear that this not the case. She DOES become flustered when she sees Iide's penis in episode 2. So she is capable of feeling embarrassment or shame. However, she ALSO is capable being turned on. You see, Hidomi is a Nightmare Fetishist. She gets a nosebleed seeing Iide getting beat up, and her dream of being devoured to death as a zombie was apparently "this" close to becoming a wet dream, considering that she woke up blushing instead of horrified. Hell, her dreams in general are dark and violent, and in her episode three dream, she outright fondles herself at the thought of being violently devoured. Not only that, but she outright "overflows" when she is told that staying with Haruko will get her killed. Hitomi has both sadomasochistic tendencies and fetishes; she is turned on by watching others get hurt, but is also turned on heavily by the act, or even just the threat, of death or pain caused to herself. Normal porn doesn't get her riled up because it doesn't DO anything for her. Her fetishes are more extreme. In fact, it is quite possible she is an avid porn watcher at home. It would explain her lack of expression during Haruko's impromptu class-wide porn session, but also her extreme fetishes; the more you watch porn, the more desensitized you become, to the point where people find themselves needing more extreme porn to get off, like BDSM for example.
The whole meaning of the catchphrase in Progressive's final episode: "It doesn't matter." Some may easily draw the conclusion of the second season not mattering as a whole in the grand scheme of things. But it takes a whole new meaning when you realize the meaning of Hidomi's character development is not living in the past and staying focused in the present. What happened in the past doesn't matter because you can still change in the present. In that way, you will have a brighter future for yourself. When Hidomi moved on from her father's disappearance and came to terms about who she was, she became a much happier person who was able to connect with people. It mirrors Naota's catchphrase in the original: "Nothing ever happens here, everything is ordinary". From the beginning, FLCL has always been an ordinary coming of age story with extraordinary events happening. Progressive is all about moving on from the past and living for the present to create a future.
This adds a layer of sadness to Haruko's character because in spite of knowing that she might be a happier person in letting Atomsk go, she chooses not to progress and continues to chase him anyway. Jinyu is a reflection of the more mature and accepting side of herself that she chooses not to accept. The good news is that if you consider Alternative to be connected with Progressive, then Haruko not wearing the bracelet that connects her with Atomsk is gone and shows that she peacefully connected with Jinyu and gotten over her obsession.
If one pays attention to the keychains on Ide's clothes, you'll notice that they're a set of speakers. What do speakers do? Make sound. This shows Ide's personality as an extrovert who is always speaking out with his own opinions and always trying to connect to Hidomi. Hidomi wears headphones which shows her personality as an introvert. She prefers to tune the world out with a set of headphones that doesn't even make sound and rarely interacts with people. This is because Hidomi is constantly shut out in her inner world. Ide spends the whole series speaking out and trying to connect with Hidomi who has shut the world out. In the fifth episode, Hidomi's dream reflects on how her world had expanded and found happiness through her experiences with Ide. She even took off her headphones to show that she has decided to listen to the outside world. Their relationship takes a whole new meaning when you realize that it is built on sounds and Opposites Attract.
The ending of Alternative has split more than a few hairs with Pets' unresolved character arc, especially with how she ends up stuck on Mars with her abusive father. However, given the fact that Haruko also ended up on Mars in the end, plus her own statement that she dislikes sad endings and her much more benevolent characterization in Alternative, there's a strong likelihood that Haruko may end up making efforts to repair Pets' family situation and possibly even help her reunite and/or reconcile with Kana.
In Progressive's fourth episode, part of Haruko's monologue just before devouring Jinyu turns everything about her motivations on its head. The phrasing that Atomsk "owns everything", that Haruko has a shackle that reacts to his presence and is still on her arm as always, and her aggressive attempts to seize both his power and love carries the strong implication that the batshit insane yet loveable lunatic isn't just chasing a boyfriend.
The Wham Shot of the sight of what's inside a Medical Mechanica plant has some rather dark overtones. The M.M. "Enzyme Inhibitors" technology that Hidomi wears had drilled into her skull by this point, messing with her brain and turning her into a Genki Girl with the girl implying this may have been her original self compared to her Emotionless Girl state when they're working normally. Keeping in mind that the plants are meant to "smooth" the minds of planets, and the fact that the inside of this plant has an artificial brain stem at the core as what's interfering with Hidomi, are these things intended to turn all living beings into emotionless husks?