Fandom Nod / Ascended Fanon: A minor one. The Tokiwadai Dorm supervisor's appearance changes from the Index anime to the Railgun anime. Some fans think it was change to match her looks in the manga while others think they are just two different people with the same job. Along came Episode 19, which mentions there are two Tokiwadai Dorms, which suggest there are indeed two different dorm supervisors.
From the 2nd Railgun mini light novel "Loli Kihara", aka Nayuta Kihara, a little girl who happens to be a Kihara.
Fans have also taken to calling Heaven Canceler "Dr. Gekota" from Episode 10.
Flip-Flop of God: In the beginning of the Index novel and anime, Mikoto fires a railgun which passes by Touma but in the Railgun manga drawn by Motoi Fukuyama, she fires the Railgun at him which he stops using Imagine Breaker. Unfortunately, this caused some backlash with fans since it is contested by the fandom if this is possible. To avoid this contradiction, the Railgun anime has the events that lead to the Railgun incident Retcon to an earlier date before the time of the first Index arc.
Hey, It's That Sound!: In episode 16 of the first season of the anime, the cellphone of Kurozuma Wataru (who is actually Hebitani Tsuguo goes off. If you listen to the ringtone you find that the song playing is auld lang syne.
Also Atsushi Abe (Touma's seiyuu) is Amu's friend, Kuukai in Shugo Chara!.
Speaking of Aki Toyosaki, her fellow seiyuus, Satomi Satou and Minako Kotobuki who played as Ritsu and Mugi respectively in K-On! (which Aki also voiced in), with the former voiced Edasaki Anri, one of Kiyama's students in Railgun, who looks like a mini Ritsu and the later voiced Mitsuko Kongo;, who is not like Mugi in anyway except being rich, beautiful and gifted with a well-endowed rack on a sexy body.
The Tokiwadai Dorm Supervisor in Railgun (the one who always breaks Kuroko's neck) is voiced by Hitomi Nabatame while 'her wife' Shizuka Ito voiced Kaori Kanzaki in Index.