Angst? What Angst?: Justified by Slevin with his "ataraxia". The true reason is of course that Slevin planned all the events of the movie in advance.
Although one would think it would be easier to fake being scared than fake a lack of feelings with a gun to one's head. He's also pretty quiet for a guy who is facing off with the men who murdered his parents, and against whom he has orchestrated an elaborate revenge plot. So its likely he DOES have a certain numbness toward his emotions, like his mentor Mr. Goodkat.
Funny that he presents "ataraxia" as a condition; it's a Greek philosophical concept and considered something to strive for by various Greek schools, such as the Stoics. Which suggests he has been trained to suppress his emotions.
Critical Dissonance: Most critics hated the film, or at least gave it mixed reviews (at the time of writing, it has around 51% on Rotten Tomatoes), but it's generally well liked by the regular public- it has an 85% score on Rotten Tomatoes from fans.
Magnificent Bastard: Slevin Kelevra was just a normal kid when both his parents were murdered on the orders of two mob bosses, The Boss and The Rabbi, to make an example of his father for trying to place a bet on a fixed horse race. The contract killer sent to take care of Slevin, Mr. Goodkat, couldn't bring himself to kill Slevin and instead raised him to follow in his footsteps as an assassin. Slevin spent years plotting the demise of his parents' killers with Goodkat's help, killing the Boss's son and both bosses' book keepers to make them even more paranoid of each other after they had already previously broken up their partnership. Goodkat then kills Nick Fisher so Slevin can pose as Nick's friend and be taken to the bosses to settle Nick's outstanding debts to both men. Slevin makes himself appear harmless before later killing the Rabbi's son as well and faking his own death, then kidnapping both mob bosses and suffocating them to death after explaining his reasons for wanting revenge. Slevin demonstrates that a dish Best Served Cold requires real mastery of the Kansas City Shuffle.
One-Scene Wonder: The opening story-within-a-story has plenty of these; the casting directors did a hell of a job on the side characters.
Shout-Out: Perhaps it's a coincidence that The Boss is an avid chess player, and Morgan Freeman once played a character who hated chess.