During Ito's game at the regional tournament, both Ito and Martinez say that he is in "Zugzwang". However, in a real "Zugzwang" situation, a player loses only because he is forced to make a move, while Ito lose the same way even if it was his opponent's time to move, as he could take the pawn on d3 with the queen.
While in the class, Martinez tells the students that chess was "modernized by a Spanish named Maura", when Maura (who was actually a Puerto-Rican) in fact did not modernized chess but instead created one of the hundreds of lesser known chess variants which he called "Modern Chess".
In the school tournament, Ito tells his opponent that is a "mate in 4", which is true for that first position. However, when making his second move, his king is already on a different position than it was on the previous move (first it was on f6 but then on g6, the square from where he moved the bishop in the first place). After the girl move her king, he moves his king to g6 (in his third move, despite the fact it was previously shown there), and then checkmates on the fourth move. However, considering the initial position and the moves shown, he would have failed to force the mate in four after his second move (bishop to b3, which shouldn't be the correct one to achieve it), as she could have played her king to h7 then and delay the mate to one more move than the initial four. However, as his king is incorrectly shown at g6, the move king to h7 seems (incorrectly) impossible to play by her.