Arc Fatigue: In season 2 of the anime, Mikoto's side of the Sister's arc takes 15 episodes (Episode 2 to Episode 16). While it is widely agreed to be better than the Index version of the same arc in nearly every way, the fact remains that the majority of the audience already knew exactly what was coming, so it was a bit frustrating it was dragged out so long.
Thanks to the Railgun anime, Saten Ruiko has become one of these. Her fans find her a refreshing character among the Four-Girl Ensemble due to being an Audience Surrogate with no powers, to the point where she was popular enough to make it to the Top 8 during Saimoe 2010. Her detractors call her a blatant case of This Looks Like a Job for Aquaman, being put in plot-relevant situations to look good at the expense of the competence of the other main characters no matter how little sense it makes.
Haru'ue is not the most popular character, but she's pretty well-liked in the community. While she's not quite hated, she has a bigger role in the second half of the first season than most people would prefer, largely because she was basically created just as a device to connect Kiyama's children back to the plot.
Touma from the main Index anime is disliked by some fans loyal to the Railgun series, being a Spotlight-Stealing Squad in the first half of Season 2 who hijacks Mikoto's plot in the Sister's arc. The fact that he fights and defeats Accelerator, with Mikoto acting like the Damsel in Distress who can't do anything without him, really doesn't help. Of course, the Sisters arc was originally Touma's story in Index, giving more details on Mikoto and the Dark Side of Academy City. The Railgun version was written as a Perspective Flip; we knew from the start she wasn't the one who solved the plot. And, contrary to this opinion, there are a lot of people who loved his beatdown on Accelerator and found that totally awesome, even claiming that the reason why the Sister's arc in Railgun was so good was precisely due the final battle between Touma and Accelerator (who also looks much better animated than the one from Index), between other reasons.
The anime original arc that ended season 2 has caused a lot of division among fans. Many finding the camp and Power of Friendship levels over the top, being angered at how Misaka was given the Idiot Ball a couple times, and expressing frustration at the many plot holes in the arc. Others absolutely loved the arc since it addressed the primary problems of the Sister's arc (notably Misaka not going in alone) and everyone getting a chance to shine against STUDY.
In general, the fillers JC Staff made for the series are very polarizing. While one group of fans liked them because they gave screentime to the other characters not named Mikoto and enjoyed the Slice of Life scenes of those episodes, another fans found them annoying, pointless and boring. It doesn't helps some of them came off after the Sister's arc, who is considered by the majority of fans as the best arc of Railgun and one of the best of the entire Raildex universe.
Kihara Gensei, the patriarch of the Kihara family, is responsible for nasty experiments on children, which resulted in many of them suffering permanent trauma, all so that he could create a powerful Level 6 Esper. Gensei has no compunction murdering people in his path. The first "sample" of his experiments was his own granddaughter: Gensei overloaded her mind to collect samples from her, and repeated this process on other children as well. Gensei was fond of manipulating his own family members into becoming his test subjects, even though he knew that a massive surge would possibly destroy all of Academy City.
His granddaughterTherestina Lifeline is just as cruel and twisted. Wanting to follow Gensei's example, Therestina abducted children and put them in comas so she could harvest the samples from their minds. Gensei manipulated the young heroines into providing cover for her, all the while intending to overload the minds of the children she kept under sedation, fully aware this would destroy all of Academy City and not caring as long as she achieved the "perfection" she hungered for.
Draco in Leather Pants: Misaki Shokuhou. This is probably the only reason why she appears right from the start in Railgun S.
For Gensei Kihara, having 10 kids forcefully overloaded with esper powers definitely crosses the line. And before that, using his own granddaughters as the subject of his experiments. One was involved with the Level 6 overload experiments, the other became a cyborg!
Therestina Lifeline Kihara planning to overload the child Errors that her grandfather created so she can become god and destroy the entirety of Academy City to boot. On top of maliciously manipulating the cast, practically turning Uiharu and Kuroko against each other, and her brutal beatdown of Misaka after she used her Kryptonite Factor on her.
While Index was a hit, Railgun was more popular, sold more DVDs and got a better reception with fans thanks to a lot of Character Development for the cast. Note that this is only true of the Index anime. The Index novels sell hundreds of thousands of copies and are the most popular medium of the entire verse by a healthy margin.
Probably because it's also partially a Schoolgirl Series. Furthermore, in a world where crazy people wields crazy superpowers that get thrown around with reckless abandon, the main characters of Railgun seem like relatable humans (see the case with Saten, above).
Padding: The anime increases the importance of Saten and Uiharu, adds a fifth girl from a filler arc and then has the three of them, Kuroko and Mikoto frequently wandering around making small talk and eating things. Not much of this is really relevant to the ongoing plot arc, so when an arc gets into full swing, the three less important girls tend to get brushed aside so that the original mood of the story can remain intact.
The Scrappy: Because of her actions at the time, Uiharu was absolutely loathed by the fanbase throughout most of the final episodes of the first Railgun anime season, namely her constant Wangst and denial of Haru'ue being the cause of the Poltergeist occurences, despite the fact that the evidence can be seen with a naked eye. It was only when Kuroko gave her a much needed slap-in-the-face that people started warming up to her again. It also helps that this took place in anime-original content; giving Uiharu a free pass despite her actions.
The Woobie: It’s very hard to not feel sorry for Mikoto in the Sisters arc. It is already hinted in the Index version of the arc, but we only find out about how much trouble and suffering she went through when the Railgun version comes. From finding out about the truth of the inhuman Level 6 shift project she agreed to help with as a child (it doesn’t help that it was disguised as a cure for muscular dystrophy— a very well-meaning intention), witnessing the clones of hers being brutally murdered, her attempts of desperately trying to stop the project (which involves her sacrificing sleep and food, as well as risking herself getting beaten down by the ITEM squad), finding out that her efforts did little and just barely slowed down the project, to her finally breaking down from all the guilt and despair she suffered, and even contemplates suicide for it if it wasn’t for Touma stopping her. At this point, you'll just want to give the poor girl a hug and tell her that everything is going to be okay.
The Sisters count too, considering how they were created just to be brutally murdered by Accelerator in the Level 6 Shift project. This is especially apparent in the flashback of the first clone’s death, where she mumbles something amongst “is this death…?” and “cold…” as she is slowly dying. 9982 probably gets the worst of them all, what’s with her leg getting ripped off its place (doesn’t help that she is shown to be visibly pained during that moment, and this is especially jarring considering she shows little emotions before) and her smiling while holding the Gekota pin Mikoto gave her beforehand before getting crushed by a train locomotive.