In general, Season 1 reuses several plot points from School Idol Project as a way of showing how both groups are different in a fundamental level as a consequence of their setting and characters.
Just like Honoka, Chika decided to become a school idol after seeing a school idol performance at UDX. The difference is that instead of seeing A-RISE on the big screen, she saw µ's.
In Episode 1, Dia's set of questions are all trivia related to key events in School Idol Project.
The lyrics of "Yume no Tobira" about believing in yourself and having the courage to stand up after getting lost as you chase your dreams inspires Riko to become a school idol as a way of coping over her Performance Anxiety on the piano.
Ruby uses the story of "Love wing bell" Rin to convince Hanamaru to join Aqours.
In Episode 10, Dia somehow acquires Umi's training plan and suggests to everyone that they use it to win Love Live.
Season 2
The first episode re-enacts the scene in which Riko attempts to jump off the pier in Season 1, but this time it's Chika jumping and Riko catching her.
Chika's "normal monster" act from the first episode is referenced twice; first by Riko in Episode 1, where she does something similar to cheer up Chika, and later in Episode 5, where You does the same to encourage her.
After Chika regains her spirits in Episode 7, You and Riko ask her if she's giving up. This question in different context was used a few times in Season 1.
Episode 8 recycles a gag used in Season 1 Episode 10.
Hanamaru: Seconds, zura! Yoshiko: Already!?
Episode 11 is full of references to Season 1, between Mari making an upgraded version of her Stewshine called "Stewshine Premium", Mari using her big red approval stamp (on people's foreheads), Riko's doujins, and You standing on a box and advertising for the School Idol Club.
Episode 12 is even more stuffed with references; in addition to reflecting on every character's development up to that point in the story, there are lots and lots of details, such as Hanamaru's "Back to the Piyoko Manju Part II" (and someone else eating it), the voting paper from Aqours' first live performance in Tokyo, Riko playing "Omoi yo Hitotsu ni Nare" on the piano, and a recreation of the UTX jumbotron scene from the very start of the series.
The finale amps it up even further, including a scene where Chika remembers the various little things that happened during their time at Uranohoshi, and the entire ending song, "WONDERFUL STORIES", which consists of Aqours referencing almost every single insert song in the series note The only insert song missing is "Kimi no Kokoro wa Kagayaiteru kai?" (and related events) while dancing in the respective outfits.
The Movie
Mari's mother uses the same introduction scene that her daughter did in Season 1.
You and Tsuki diving for the thrown uniforms is a reference to a similar scene with You in Season 1 Episode 9.
As a sort of Book Ends, Aqours goes back to Uranohoshi by bus. The scene is a remake of the intro to their first PV, "Kimi no Kokoro wa Kagayaiteru kai?", except that instead of occurring at the morning when classes start, it takes place at sunset when classes end.
The silhouette shot after visiting Uranohoshi is a reference to the Season 1 opening, "Aozora Jumping Heart".
Others
The PV for "Mitaiken HORIZON" opens with the settings for "Kimi no Kokoro wa Kagayaiteru kai?", "Koi ni Naritai AQUARIUM", and "HAPPY PARTY TRAIN" appearing in order alongside their respective centers (Chika/Riko, You, and Kanan). The PV also references various scenes in the anime and animated PVs that feature Hanamaru.
The Take Me Higher Project theme song, "JIMO-AI Dash!", is the first song to feature the Duo-Trio Vol. 1 singing formations since the release of the "Duo-Trio Collection Vol. 1" CD. Also referencing the other song with "Jimo-Ai" in the title, Yoshiko and You star in the opening lines.
