In Japan, she is sometimes called "Anko" based off an initial misreading of the characters in her name. As a reference to this, some American fanworks have used Anko as the name of Kyoko's dead sister, before it was revealed to be Momo.
"Urobutcher" for the scriptwriter, Gen Urobuchi, himself. Because, well...
(WARNING: There's a Higurashi no Naku Koro ni spoiler within the spoiler tags as well) Mahou Shoujo No Naku Koro Ni ("When the Magical Girl Cries"). Originally partially a gibe at the many times Madoka is seen crying onscreen and partially a speculation on a possible presence of time loops, the nickname gained more currency when the latter was proved to be correct.
Similarly Penitent Gretchen. The name Gretchen is self-explanatory if you are familiar with the show. The title of Penitent isn't, which means "feeling or expressing humble or regretful pain or sorrow for sins or offences". It explains Madoka's temperament at the time of her wish. Also, the full name is yet another reference to Faust ...or more appropriately, how Gretchen saved him.
Legion Arrow for Godoka's huge arrow attack in Episode 12. due to its resemblance to Taskmaster's hyper combo of the same name.
It's not uncommon to see the characters referred to by their meduka meguca names, usually in all-lower case. So magical girls are called meguca, and the characters themselves are meduka (Madoka), hameru (Homura), seyiku (Sayaka), mumi (Mami), and coobie (Kyubey). The only one who seems to avoid this is kyaku (Kyouko).
The show and its protagonist, Madoka, tend to be referenced as Doka by some fans.
Foreshadowing: Entirely a pure coincidence, but the editor of one standard critical edition of Faust, Cyrus Hamlin, passed away on January 19, 2011; one day before episode three aired. It's pretty creepy honestly.
Perhaps more amusingly, he also voiced one of the abusive boyfriends Sayaka encounters in episode 8, resulting in his own website's credits page listing his roles in the series as "Tomohisa, pimp".
Lying Creator: Gen Urobuchi shortly before the series premiere: "I have been entrusted with the formidable task of series composition and script for all episodes. Although having director Akiyuki Shinbo and Ume Aoki-sensei as teammates puts a great deal of pressure on me, I will do my best to deliver a heartwarming, happy story to our viewers!"
Gen Urobuchi wants to write stories that can warm people's hearts... But ever since I can't recall when, I can no longer write works like this. I have nothing but contempt for the deceitful thing men call happiness, and have had to push the characters I poured my heart out to create into the abyss of tragedy...
Urobuchi later confessed that he lied to retain surprise Episode 3. The original plan for the production team was to hide Urobuchi's involvement with the show, so when the staff list was leaked he tried to do damage control. Now that the cat is out of the bag and it's clear nobody believes that he reformed: "Okay now I've took a big load off my mind. Thank you everyone who keep up until today! I'm going back to the normal Urobuchi from now on!"
Meaningful Release Date: The last two episodes were released on Good Friday, and in the finale Madoka sacrifices her existence to become a god and save the souls of all the witches. And it wasn't even intentional, it was because of the March 2011 tsunami in Japan which pushed back the final two episodes.
Also, Mami's surname is probably a reference to Tomoe Gozen, a famous female samurai from the late twelfth century who supposedly fought in the Gempei War. Doubles as an Ironic Name, since Gozen is also supposed to have survived that war.*
Interestingly, Gozen herself seems to appear later in the series, briefly, as one of the historical magical girls in Kyubey's flashback.
A wall in the abandoned building in Episode 2 has graffiti of text lifted verbatim from the original German edition of Faust. Creepy.
The fight between Sayaka and Kyoko in episode 5 is reminiscent of Saber and Lancer's first fight in Fate/Zero, another of Urobuchi's works. Though the sword-wielder puts up a valiant effort, they lose the fight's advantage due to the spear-wielder's craftiness with their weapon, and are ultimately saved by a Big Damn Heroes moment from another fighter.
Episode 9 has Madoka's room filled with all kinds of different chairs, a Shout Out to Bokurano.
Episode 9 also features some graffiti that reads "Love Me Do".
In the OP while Madoka is reflecting on her adventures as a magical girl, Madoka is seen striking 3◊ famous◊ poses.◊
In the final episode, when Madoka goes around purifying all of the magical girls who are about to die or become witches, the way that she appears in front of them and makes them fade away, taking them with her is awfully similar to the Instrumentality sequence in End Of Evangelion (Everybody Hugs and Turns Into Tang). Similarly, Madoka's wings when she takes out her witch are somewhat like Reilith's wings.
Madoka picks a red ribbon over a yellow one in the first episode. Taking this as a reference to the yellow-ribboned Haruhi Suzumiya might seem like a stretch, until Madoka becomes a nearly-omnipotent Reality Warper and attempts to recreate the entire Universe...just like Haruhi. The red ribbon also achieves similar iconic status when Homura wears it.
Word Of God has stated Episode 10 was actually cut down in size, and would have originally been 45 minutes long.
According to the official guidebook, the original proposal for Madoka had thirteen episodes instead of twelve.
As seen here (major spoilers in link), the audio Drama CDs were originally going to be quite different. Even in the final product, a line got cut from the first Drama CD: Madoka shouting "Finitora Freccia", which means Finishing Arrow in Italian.
The shopping mall Madoka, Sayaka, and Hitomi visited in Episode 1 is a blatant rip-off of the Weltstadthaus. There are actually extremely glass-y buildings in the world!
Weltstadthaus means "global-city house". According to The Other Wiki "global city" is defined as a city where happenings in it affects the world (due to the city's economical/strategical/magical importance), i.e. Alexandria in the ancient world or New York in the modern world.
The sixth◊ is by Hajime Ueda, who created the FLCL manga and the art for one of the Bakemonogatari endings, among others. A touch of Fridge Horror: The girls are all solid black, with their Soul Gems the only thing being illuminated. They also form the Kanji for death◊ when flipped 180 degrees.