Batman Gambit: Toma employs this at the climax of the first chapter. He bluffs the suspect by pouring liquid that he says could trace the culprit's name. The liquid is just water, but the suspect scrambles it out of fear, proving himself as the culprit. The bluff will falter if the suspect maintains his cool just a little bit longer, but as Toma says in the conclusion, only machines are completely controlled by logic.
Child Prodigy: Touma has a BS in physics before the others even started high school.
Church of Happyology: During one of Touma's flashbacks, District Attorney Annie Craner was assigned to prosecute a widower who is accused of murdering her husband so she can inherit his fortune to continue paying for the self-help cult-like group called "The Path to Arcadia", an organization she is a part of. As the trial continues, the group sends death threats to Annie, protest against her and accuse the prosecution of a Witch Hunt. Then one of the widow's friend, an old lady, shoots her when the case is about to be finished. She seemingly was killed. Well, not. It got stranger from there, with her father involved.
Mind Screw: In Chapter 38 where the bosses of Shanghai mafia kill each other. According to the witness, the last boss killed is murdered by the first boss killed. The truth is, Toma's friend, Hu Jia Hui, has feigned the death of the first boss in order to incite a Cycle of Revenge that destroys the mafia. Then who kills Hu in the end?
Viewers Are Geniuses: This is probably why it took so long to get scanlated, since many of the terms are just too... advanced for someone who didn't take university.
The Watson: Kana plays this role, but rare for the genre, Kana is shown to be able to pretty easily follow Toumas train of thought and often helps solve the case just as much as Touma does.
Even then, that's because Touma takes time to explain things to Kana (he figured out she will be more helpful if she gets what she was doing) and even then, sometimes if the explanation involved advanced science (like mathematic, for example)... yeah.