Tokyo ESP is a potential wasted in the very worst way. It's opening episode sets the bar high and then the rest of the episodes proceed to let you down, time and again, on every front. It sets itself a nice, not too high bar with a very deceptive first episode, and proceeds to lower that bar until it's burrowing to the center of the Earth.
It is a wasted potential, plain and simple. Things could've been wonderful. But as it stands, they're not.
Story: It's all-out war - people with psychic powers, whom have taken over Tokyo and have intentions to take over country, have declared themselves homo superior. Rinka, who, like ever other esper, got her powers from a glowing fish that only she could see (or rather, only espers could see) is there, with a few friends, to put a stop to their reign of terror.
So far, so good. The show starts in medias res, and then takes you back to where Rinka first gets her powers, and proceeds to show you to lead-up to the showdown. There are some backstories given, especially one that explains the villains' motivations (which are understandable, of course, but... we'll get to this below.)
Execution: Sloppy. Starting in medias res and then immediately jumping back to tell the story of how we got here is fine, but starting with an action-packed, battle-for-the-planet episode and immediately shifting to comedy and staying there just brings disappointment. It takes a good long while (read: the entire series) for Tokyo ESP to ever feature any kind of decent action. The high-octane, anime-blood-splatter-fest with slightly political undertones that grips you in the first episode is replaced by tame lives-of-espers bits.
Another minus in this front is that at the last possible second, it throws something massively important for the story, so much so that our designated villain remarks we are finally at the point of everything, at the what it's all about. What that is, I don't know, because we never learn. We get a seven-day time-skip instead. Imagine if in
If it was an attempt to wax philosophical about how sometimes there is no point, I'd love it, but it's not. They just run out of space (and ink, too, didn't you.)
A further jarring aspect of the anime is that as it goes on, the secondary characters tend to get more bizarre than is called for (goddamn Roshi), deus ex machina are pulled out of consenting butts by the dozen (the telepathic stork, for instance), and at one very crucial point, the power of a main character is played very loosely; a case of Powers as the Plot Demands. Luckily, the last one is actually a plus and is logical enough that it sits well. But the rest, just... bleh.
Having a midget in a panda suit for a martial arts trainer, who used to train cops, such as Rinka's father is a pointless visual gag - there is no reason why he can't be just a guy.
Heroes and Villains: Just no. For one, the heroes are clear-cut, "champions of justice" types, and the one hero that isn't, is recruited because she has the hots for Rinka's dad. Rinka may be commended for her determination alone, but she's a two-dimensional designated heroine. Which is actually what every other hero is.
The villains are cardboard "yarr, I'm evil" types. A sin that the series commits is that the Professor's tragic origins are completely negated by his monstrous actions, to the point where you get apathetic towards him - he's the main villain, yet it's difficult to care if he lives or dies.
Minami is atrocious beyond belief. Thing is, this character could have been wonderful, and there are ideas thrown around (at the last second), but instead, she's so annoying with her mere presence that it's impossible to think of her as anything but a brainless minion. The exceptions to that are few, and brief, and the same thing that marks her as a could have been is what ultimately makes the character unbearable.
Animation: Is it me, or is this anime, despite the glossy coloring, very poorly animated? The first episode is so far above the rest of it that one wonders if that's where all the budget went to. Some secondary characters (Nabeshima for instance) are downright ugly to look at. The lines are too sharp, most of the character designs are good but too basic, bystanders are poorly-drawn, anyone outside the inner circle is an eyesore... it gets worse and worse as the series goes on.
Sound: Applause to the seiyuu who have managed to keep their tone serious while a lot of lollygagging is going on. Nice enough soundtrack, some good rock tunes. Nothing else to say.
The Part that I Said We'd Get to in the Story: The motivations of the Professor are completely irrelevant. The guy who executed an overarching, long-term plan; who is responsible for every event being put into motion is worthless as a character at all because of this. The near-full episode wasted explaining how he got to be who he is, is a filler episode with nothing of consequence or importance or of note in it. It's a waste of space.
Why?
Because we never get to see what he was aiming for.
Since the series sees fit to cut out before we can learn what he intended to do, and why, this means we were just wasting time showing background decoration to a villain whose efficiency is admirable but whose mere existence is negated by the fact that we never find out what he was after. He gives a few mission statements, of course, but these mission statements are utterly and completely worthless, as they do not relate to what his real plan was.
In short, you can cut the villain out completely and not lose much, because his shoes can be filled by a more coherent character, easy.
Overall: I watched it, but I had nothing else to do and no other series I wanted to engage. Would I recommend it? Give it a try. I was bored through most of it. Someone might like it. Just not what I expected.