Theme Naming: Each of the main protagonists has a surname (Kaname, Miki, Akemi, Tomoe, Sakura) that can also be used as a given name. Doubly so in Homura's case—her last name is usually a first name, and vice versa.
Theme Tune Cameo: Madoka listens to "Connect", the opening theme, at the record store in the mall in Episode 1. Episode 6 also features Kyoko dancing to a techno version of the song on a DDR stand-in.
Becoming a Magical Girl automatically detaches the girl from their loved ones but all girls have Phileo love (friendship) as a main motivation.
Madoka almost became a magical girl (thus accepting a Deal with the Devil) to rescue her friend. In the last episode she demonstrates Agape love in her wish to rewrite the laws of the universe so no magical girl will have to suffer turning into a witch by absorbing all of their despair.
Too Happy to Live: The creators did this with Mami Tomoe who died while deliriously happy at the thought of a Lovely Angels partnership with Madoka. Don't go thinking they won't have the guts to do it again.
Took a Level in Badass: Homura Akemi started as a frail and nervous student in her original timeline, but has steadily become tougher and more confident with each timeline, thus resulting in the Homura that we know.
Took A Level In Cynicism: Flashbacks reveal that Homura started the series as cheerful, klutzy, and a Wide-Eyed Idealist. Repeated failures to save Madoka in timeline after timeline caused her to slowly withdraw her faith in the world, turning into The Stoic character she is today.
Tragedy: It's a complicated case. In the classical sense, a tragedy is when the protagonist dies. Madoka Ascended to a Higher Plane of Existence and so she's technically dead but still around because there are no more witches. In a broader sense, everyone is better off at the ending then they were at the beginning; even permanently dead Sayaka is keeping Madoka company in magical girl heaven.
Tragic Hero: Sayaka does everything in her power to be a force of good, but collapses when she couldn't forgive wrong doings of others as well as her own.
Transformation Sequence: While this is a Magical Girl show, these sequences are done in very sparse quantities, very quickly, and for each girl the sequence appears once or twice in the series (most "transformations" are simply a more realistic rendition of the girl briefly glowing and reappearing in new clothes). They are also not done consistently, averting Stock Footage, and are very rare; for a while, only Mami's, Sayaka's, and Kyoko's could be found. We finally see Homura's in Episode 11. Madoka never gets one, unless you count the one from the intro for Episode 1.
Transformation Trinket: The girls use their soul gems to transform into magical girls. Inverted. It's not so much that they use the soul gem to transform their bodies than they use their bodies as vessels into which they project their souls, as it is the soul gem, not the body, which contains the magical girl.
Madoka goes through this largely by watching people she cares about either die or turn into a witch, with her being unable to anything about it, largely due to Homura keeping her from making a contract.
Sayaka first fights against Kyoko, who berates her for using her wish for someone else rather than herself, then finding out what happened to her body/soul when she became a magical girl. Then her friend Hitomi mentions that she's interested in Kyosuke as well, and will ask him out after giving Sayaka one day to confess her feelings, which Sayaka doesn't do because of her body/soul situation. Finally, she hears of two guys who are making fun of a woman one is dating, and thinking she's a moron for devoting herself to him, which Sayaka doesn't enjoy hearing, and finally gives up all hope and turns into a witch.
Kyoko first witnesses her father preach heresy which causes people to stop attending their church, and then their family starts to suffer lots of hardships, including starvation. When she makes her wish to have people attend the church, at first it seems good, until her father finds out what she did, and he kills himself and the family as a result. She finally sacrifices herself to stop Sayaka who just turned into a witch.
Homura is repeatedly forced to watch Madoka die, or turn into a witch, and whenever she tries to warn them of something bad happening if they become a magical girl, they either ignore her warnings, or take it a with a grain of salt. Most of the time the main characters view her in a very negative light, and it isn't until Episode 10 where we see why Homura acts the way she does, due to her inability to change the fate of people around her, including the person she cares about the most, Madoka herself.
Unwitting Instigator of Doom: Amy, the small black cat from the opening that doesn't appear in the series, but is explained in the first drama CD. Madoka has contracted because of her in the first timeline, to save her. Not only that, the cat has also led Homura to dead Madoka after her fight with Walpurgisnacht, kickstarting the whole plot.
Kyubey needs Magical Girls to fight Witches; he also needs Magical Girls to become Witches.
Homura goes back in time whenever Madoka dies. Not only that, but Homura goes back every time to make things better. Every time she goes back in time it gets worse so she needs to keep repeating the cycle, or become a Witch.
Villainous Breakdown: A very minor one from the resident stoic, but still, Kyubey's reaction to Madoka finding exactly what to wish for in Episode 12 was satisfying.
Visual Pun: Minor, possibly unintentional example: in the first episode, Sayaka uses a fire extinguisher on Homura. "Homura", written a certain way, can mean "flame" or "blaze".
Wake Up, Go to School, Save the World: You can probably guess what they do to this one. Initially, it seems like a possibility, but witches are so dangerous and Grief Seeds so vital that "normal life" takes a distant backseat for most magical girls in the quest to stay alive.
There is even a line in which Kyouko questions how Madoka could be going to school, after the events of the previous night.
Walking the Earth: Homura in the ending; fighting demons who are the new manifestation of despair to feed Kyubey and protect the world that Madoka left.
War Is Hell: One of the harsh realities about being a Magical Girl that hits the heroines hard, especially poor Sayaka. Battles are painful and traumatizing and if/when a magical girl dies, no one will ever know because of the witch's barrier.
Episode 3. You will NOT be ready. To recap — the first few episodes were ominous, but mostly standard Magical Girl show fare, leading to lots of fan theories. They had no ending credits montage nor ending theme, relying on the credits showing as the story continued. After the events of Episode 3, we have a fairly good idea where the deconstruction elements lay, and the show now officially has an closing-credits sequence. It's creepy as hell.
Another one happens in Episode 6. Not only is Sayaka getting more and more hyped up in her rivalry with Kyoko, but when Madoka tries to stop her from fighting via throwing her soul gem away and hoping to strip her of her powers ... it's shown that if a Magical Girl loses said soul gem, she will become an Empty Shell. So no, there's no way to get the fuck out of the contract, until she dies. Ouch.
Another one happens in Episode 8. Homura is confirmed to be from an alternate timeline. Sayaka's soul gem goes fully dark, turning into a grief seed, which then explodes and turns her into a witch. This is how all "true witches" are created. Kyubey knew this from the beginning and ends the episode with the Wham Line below.
In Episode 9 it is revealed that Kyubey is an alien who is using the energy released from magical girls and witches to prevent the universe from dying. Also, Kyoko sacrifices her life to kill Sayaka.
In Episode 11 Kyubey points out that all the time traveling has inadvertently given Madoka all the magical power of all her previous incarnations, which due to Homura's "Groundhog Day" Loop, are legion; meaning she's destined to be the most powerful witch ever, and every time Homura tries to fix it, she makes it worse. Speaking of Madoka, she shows up at the very end, causing divergence from the foreshadowing of Episode 1, and announces her intent to make a wish.
Kyubey: Oh Madoka, that was really bad. Madoka: Huh? Kyubey: What's wrong with you, are you out of your mind? How could you throw your friend away like that?
Kyubey:Since this country calls women who are still growing up shoujo (少女 girls), then for girls who are on the way of becoming majo (魔女 witches), it's logical to call them mahou shoujo (魔法少女 magical girls).
From Episode 8 as well:
Homura: I'm going to do whatever it takes to stop you, Kyubey, or should I say, Incubator.
Kyubey: The truth is you humans would most likely still be living naked in caves.
Kyoko:You bastard! What have you done!? You scumbag! You've turned us into zombies! Is that what happened!?
It makes much more sense when you consider that Kyoko's father was a priest; her revulsion stems (at least partially) from her religious upbringing.
What Is One Man's Life in Comparison?: Kyubey's rationalization of the events. Witch energy is used to prevent, or slow down, the universe's entropy. Those that meet the requirement to provide a good amount of energy in exchange for a wish should not really object to it as they would be helping all the other lifeforms in the universe. Kyubey even insinuates all of human history has revolved around magical girls and their wishes, and later falling.
While it isn't obvious at first, the plot is essentially that of Goethe's Faust: Eine Tragödie, with Homura as Faust, Madoka as Gretchen (her witch form's name references this) and Helen-of-Troy (& Euphorion), and Kyubey as Mephistopheles. We don't see it in full until late in the series because the plot is told from "Gretchen's" point of view.
Sayaka's story arc is essentially The Little Mermaidbad ending and all, with Sayaka (the Mermaid) giving up her original body (in a sense) for Kyosuke (the Prince), only for him to go after Hitomi (the Princess) instead. This is all-but confirmed by the fact that Sayaka's witch-form has a mermaid tail.
The fact that Sayaka later ascends (or something, it's vague) with Madoka is reflective of Andersen rewriting the ending of the tale so that the Mermaid eventually earned a soul and was able to go to heaven.
Wishplosion: Madoka's wish rewrites the laws of the universe so that magical girls don't turn into witches when their soul gem expires; they vanish instead. By doing this, she even safeguards herself by erasing her own witch form.
This is Kyoko's attitude after becoming a Magical Girl. While she initially was an idealist like Madoka and Sayaka, after her life was ruined she decided to only use her powers for her own benefit. Yet another reference to Faust...
Insofar as Kyubey is concerned, the "become a magical girl" process involves a lot of this. He's very quick to point out later on that the "detached soul" thing makes their human bodies virtually painless and nigh-invincible (Mami only dies in Timeline 5 because her soul gem is crushed in the same act that ruins her body. The only other time we see non-witch magical girls die are when their soul gems are violently destroyed) and gives them superpowers. He doesn't understand why they freak out about the soul separation, because as far as he's concerned, even with the whole "fight witches" thing, this "painless immortal superbeing" thing is a pretty sweet deal.
Mami, who had been played up as being powerful if not experienced goes up against the witch against Homura's express warnings, and gets her ass kicked in the most horrific manner possible. It wasn't that she was suddenly and inexplicably weak but too distracted by the happy thought of not having to fight alone anymore and started fighting recklessly.
The second example is Homura, showing up seconds later (Mami had used magic to subdue her) and beating the witch effortlessly. Justified in a later episode when it's revealed that Homura's time stopping ability is useless if she's restrained before she activates it, which is logical considering she would still be restrained with time stopped.
You Didn't Ask: Kyubey will not lie to the girls. He just withholds information unless specifically asked. He affected this defense of his actions in later episodes, but in actuality his words in earlier episodes were a case of False Reassurance. The girls asked several of the right questions early on and he gave replies that were arguably true but misleading until the girls thought they understood.
Your Approval Fills Me with Shame: During Episode 11, Kyubey congratulates Homura for inadvertently making Madoka the most powerful witch of all time by going through all of those time-loops and thereby amplifying her karmic destiny (and therefore her magical potential) every time.
In the broadcast versions, soul gems vary in size from egg to pear. They're more consistent in the Blu-Ray versions. Kyubey mentions that the size of a soul gem can depend on the Magical Girl's potential power. In the last episode, Madoka's soul gem is the size of a comet.
Kyoko's spear seems to randomly change length between shots. In a zoomed out shot, the spear is twice her height. When the shot changes immediately afterward, the spear is a more manageable length for her to spin around. There's nothing to suggest that she can change the number of segments in the spear.
Zettai Ryouiki: Madoka in her school girl outfit but the others do not. Mami, Sayaka and Kyoko in their magical girl outfits.