These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Fridge Brilliance: Every magical girl has a wish granted and at least one "bonus" power related to their wish. Satomi wished for the ability to talk to animals. That was her wish, not her power. Of course she would be able to do something else.
To expand on that, the Pleiades' powers seem to stem from the spirit of their wish rather than the words of the wish. Umika's literature related wish allowed her to read minds and rewrite memories. Mirai asked for a museum to house her teddy bears and she can summon a collection of them. Satomi's wish was to speak to animals i.e. communication. Her Phantasma Bisbiglio ability allows her to use someone as a medium to communicate through.
Dunno if this all counts as fridge; it's established in the main anime that a magical girl's powers are related to the wish.
In one of the flashbacks, the silhouette of the incubator seen with Mami at first seems to be Kyubey, only for the incubator in the flashback to then be shown to be Jubey. However, with Chapter 21 revealing that the Pleiades made Jubey, and one of Umika's spells rewrote the memories of magical girls in the city to view Jubey as the incubator they had contracted with, this means that it likely was Kyubey who really appeared in the flashback. This also explains why Kyubey was partially obscured in the flashback of Airi making her contract.
Then there's the sudden witchifications that take place in the story to the point of a Diabolus Ex Machina. Anri, Satomi, Niko, Saki, the Soujus and the gems in the Freezer. Chapter 21 reveals that instead of completely purifying Soul Gems, Juubey could only clean the surface meaning that girls thought that their gems were clean when in reality, they were still dirty hence the constant witchifications. Fridge Horror when you wonder how many Puella Magi turned into witches because they didn't remember to use their Grief Seeds to clean their gems and because the local Incubator Jubey couldn't purify their gems. And judging from all the darkened Soul Gems in the Freezer, probably a lot.
Fridge Horror: When Madoka rewrote the universe, she only changed the fact that Magical Girls turn into witches. This means that Kanna Hijiri will still be created in the new universe from Niko Kanna's wish. It might not happen, but the possibility still exists...
On the other hand, the possibility of Kazumi existing in the new universe is definitely nil. Since witches don't exist in the new universe, the Pleiades wouldn't be able to make witch clones of her as they did in the old universe. Plus, the Pleiades would probably be more capable of coping with her death if/when she faded since the Incubators actually warn the girls about that before the contract instead of finding out about their fates as an Awful Truth.
According to Jubey, Kanna was created as a way for Niko to see what her life would have been like if she hadn't accidentally shot her friends when she was a kid. However, doing that meant letting Kanna take her place among her family & friends while Niko would've had to avoid coming into contact with them to keep up the deception. How badly would her psyche been affected by that incident if she was willing to remove herself from everyone she's known just for a glimpse at an alternate life? For that matter, where has Niko been staying while Kanna was substituting for her?
Genius Bonus: The Pleiades Star Cluster is in the Taurus constellation. The constellation after that is Gemini. The villains include Airi, who wished to become Yuuri, the Soujus, who are two magical girls in one body, and Kanna, who was a copy of Niko. The magical girls who fight against the Pleiades' Saints can all be thought of as twins.
There's also the duality of "old" and "new" Kazumi. Especially since the new Kazumi is a clone.
The "Angelica Bears" museum. The Angelica genus of plants contains the Ashitaba plant. It's name literally means "Tomorrow's Leaf". This is apparently a pun on Mirai Wakaba's name, which literally means "Future Young Leaf".
Growing the Beard: Grew some stubble in Chapter 4, and seems to have a full beard in Chapter 5.
Les Yay: There is quite a bit of this. The most obvious "couples" are Umika/Kaoru, Airi/Yuuri, and Ayase/Luca.
Airi/Yuuri: To put it in perspective, Airi became a witch because she was consumed with getting revenge for Yuuri's death. Her witch form is a giant heart. There are also clear parallels between Yuuri's wish for Airi and Sayaka's wish for Kyousuke.
In the omake comics, Saki seems to feel something special for Kazumi. YMMV on whether or not it's Big Sister Instinct.
Chapter 12 has Saki buying a very sentimental gift for Kazumi, and Mirai feeling jealous of Saki and Kazumi's closeness.
Chapter 13 has Satomi confirm that Saki loves Kazumi.
Chapter 14 clarifies the wording. Saki actually loves (or loved) Michiru, and she likes the clones. She might have been unable to finish them off because they remind her of Michiru.
In Chapter 18, when Saki becomes a witch, Mirai refuses to fight back and ends up decapitated. It's established that she had no problem fighting her friends' witches before (Niko's), but she is unwilling to hurt Saki even when she's a witch.
Not only that, but Mirai's Last Words before she dies are actually "Saki... I love you."
Moral Event Horizon: No less than three of the Pleiades Saints have crossed it as of Chapter 21. Long story short, when Kyubey (who crossed it in Madoka Magica, mind you) proves to be more trustworthy than you, you know you're past the MEH.
The official translation itself is actually a bit better at translating all the language puns. For example, the first chapter's title was the awkwardly named "Bad-Guy-Reckonoff" in the scanlation. The official English release uses the smoother "Spotabaddynoff".
It also correctly translates the Shout Outs in the Italian attack names - see the main page.