The Level Upper functions rather similarly to programs like Folding@Home. No big deal, seeing as how that was basically outright stated in the series. But the brilliant part is the reason why everyone was going into those comas after using it—the program itself was using up too many resources in the 'processors,' which led the user's bodies to shut down higher brain functions in order to avoid damage to their 'hardware' (which, in this analogy would be analogous to a computer overheating and burning out the motherboard). As such, if Kiyama Harumi had written the program to use less resources, people may not have collapsed and brought up suspicion from Judgment and Anti-skill, meaning she would have had a much greater access to more processing power for a longer period of time, with Level Upper potentially even going viral like Folding@Home did. Or, she could have been upfront about it from the beginning and tell people she was using it to find a cure to cancer or something.
Similar to a bit of Fridge Brilliance on the other fridge page regarding the Sisters, there's more regarding Harumi Kiyama. Her running gag/oddball quirk in her first episodes was her Ditzy Genius tendency to go straight to the simplest solution. She gets hot, or her clothes get messed up, the obvious thing to do is strip. Her brain doesn't consider the middle grounds at all. That very same quirk is what leads her to her Well Intentioned Extremism. She initially went for the most obvious solution, get permission to use Tree Diagram. When that ultimately failed, she took matters into her own hands and went for the plan most likely to succeed: Level Upper. The manga even lampshades this a bit when Uiharu points out things Harumi failed to consider (such as the possibility of its victims not being found or falling comatose in a place where they could be hurt).
Saten and Uiharu go and buy ice cream. Saten isn't holding on to her cone, but instead Uiharu is. Why? They're taking advantage of Uiharu's ability to keep the temperatures of whatever she touches steady and preventing the ice cream from melting.
During the Level Upper arc, when Saten gets an ability, she stares in awe at her hands as she's making blades of grass fly around them. After that, whenever they talk about the Level Upper or developing abilities, Saten will stare at her hands in the same way, only somewhat wistfully. And at least once while talking about the same things, she rips up some grass and lets the wind blow them away. Extremely subtle Call-Back.
The reveal that Misaki was friends with Mikoto's first clone explains a lot, such as why she went to all the trouble to rescue 10032. It also explains more subtle things: Such as why she was so shocked when she saw 10032 on the monitor (and why she was able to immediately recognize her as a clone, even though she couldn't read her mind at that distance).
Quite a few people wondered why the Academy City leadership didn't develop something based off of Level Upper, given their general fixation on dangerous and morally dubious methods of improving Esper powers. However, the very nature of Level Upper mandates a Hive Queen; the person who the brainwave pattern is copied from. In a citywide network with 1.8 million members (Touma's count of the number of Espers in the city; the remaining .5 million presumably are adults who never received power development and have no AIM field whatsoever, so they might or might not be able to join) the Hive Queen would be impossible to control. He or she would basically be a Level 5 in every ability, including both the ones with enough raw combat potential to wipe out entire armored companies and the telepathic/clairvoyant powers to detect any conspiracy to manipulate or counter them. Furthermore, the natural choice, as far as the citizenry at large is concerned, is Mikoto, because her power lends itself to communication, copying over her brainwave pattern might bring some of her skill at using powers with it, and she hasn't been abusing her rather substantial present power. Aleister is probably unwilling to trust anyone, especially someone as idealistic and combative as Mikoto, with that level of power. In chapter 61, this is pretty much exactly what happens, with Gensei revealing that he gave Kiyama the Level Upper data so she'd use it and generate more experimental data, and then fusing Mikoto to the MISAKA Network, which begins to turn her into a Level 6. He gets around the problem of her being Hive Queen of the network by using a Level 5's mind control on the Sisters, and controlling her through them.
Febri calls everyone by their first name, except for Uiharu (and Mikoto, who she's scared of). This is to help explain why in Index, Mikoto wasn't sure of Uiharu's first name.
In the final episode of Railgun S, Misaka 19090 thanks Nunotaba for giving her stronger emotions. 19090 also appeared in Index S2, where she was the only one of the clones in Heaven Canceller's hospital who actively dieted, in order to be more attractive to Touma. Though the clones should all have some level of emotion thanks to Nunotaba, 19090 has the strongest due to her being the first to receive the emotional programming.
In the last episode of Railgun S, Mikoto swallows her pride and asks Misaki to edit a few memories so that Nunotaba and the girls can live in peace. This is a bit of an odd choice for Mikoto (since she doesn't trust Misaki as far as she can throw her and doesn't want to be in her debt), but it makes perfect sense for Misaki. Misaki cares for Mikoto's clones due to her friendship with Dolly, so once she found out Nunotaba had worked to save them, she would be more than willing to help. In fact, this might actually have been when she found out about them.
It was believed that Mikoto's Railgun has a range of 50 meters but she proved them wrong. The belief came probably from the fact that her ammunition, regular coins, could not endure the immense heat and air drag acting upon them when fired. It wasn't her Railgun that had limited range, it was the coins that disintegrated after after travelling that distance. It is actually weird that scientists in Academy City never took that into consideration. Give Mikoto ammunition that can endure her power and she can shoot much farther. The final episode of Railgun season 1 proves this, when Mikoto shoots an object the size of a small car at an enemy, and the orange afterglow extends for quite a long distance, much further than a coin-railgun would.
In Episode 1/Chapter 1, it is stated that Mikoto's AIM dispersion field is only 18.2mm thick, and in her battle with Frenda, she says that she can use the weak electromagnetic field around her, her AIM dispersion field, as a sort of radar, allowing her to sense where things are even when blinded by a flash grenade or thick smokescreens. However, at first glance, this makes no sense as a radar with a range of 18.2mm would be all but worthless. However, it is also explained that the AIM dispersion field is subconsciously emitted by Espers and it is implied that certain people are able to manipulate theirs. Normally, Mikoto's field might actually be a lot bigger (at least a few meters judging by the range at which she detects incoming objects), but she merely suppressed it during the system scan to get a higher rating.
Mikoto is often specifically called "the Railgun of Tokiwadai" (instead of just "the Railgun"). Of course, she's the Railgun and goes to Tokiwadai, it makes sense. But in the prequel arc, we find out that she actually invented her railgun at Tokiwadai, so it also makes even more sense that a lot of people would emphasize that connection.
Imagine yourself in Saten's position, being someone in a city designed for developing abilities, without an ability. It's actually stated that the majority of the students in Academy City are Level 0, so she's in good company. It just so happens that this is one of those cases where being in the majority sucks. And it probably doesn't help that she's best friends with a Level 5 and 4. It's somewhat of a surprise the suicide rate of the city is never mentioned...
A more chilling thought is that her esper development is being secretly sabotaged. Part of doing science experiments is using control groups. Since esper powers are the result of both a drug regimen and training, it could be that she received a placebo drug or is not receiving proper training because she's in a control group, so no matter how hard she tries, she won't get powers. The worst part is that it's probably not anything done maliciously, as it could be double blind, so she has nothing to blame but bad luck.
Why does Kiyama seem so tired all the time? Ever since her students went to sleep, she's been unable to get any. This is pretty much confirmed as the students notice upon awakening that there are bags under her eyes (which weren't there when she was their teacher). When we see her in the hospital after her students were cured, you could see that the bags have disappeared. She's been able to sleep peacefully again.
The first closing sequence is a bit creepy. Mikoto wakes up to a grinning Kuroko while the lyrics describe a promise (or threat) to "always be with you" day or night.
Chapter 124 of Railgun manga reveals that Kazari Uiharu is actually capable of getting angry and holding grudges when Saten was injured by the enemy. Luckily, Saten was there to stop Uiharu before she step too far gone. With her hacking skills and Thermal Hand ability (now is possible to be developed thanks to the new AC Board Chairman) which she can use to prevent her computers from overheating, no one knows how far Uiharu will go if Saten dies or becomes vegetable.
Also in one story arc, Uiharu jokingly said that she had no need for prize money since she could easily rob an online bank dry if she really needs quick money.
(and why she was able to immediately recognize her as a clone, even though she couldn't read her mind at that distance).