Character mistake: Artie says he'll recite pi to 100 decimal places. After the first few numbers, it skips to him finishing up by saying "46375." The last 5 digits would be "70679." In fact, the sequence "46375" doesn't occur until the 95,517th position.
Character mistake: In s01e08, "Q and A", Yelena moves her bishop to B6. The announcer says that's going to win it (the game gets interrupted at this point). However, that move does not put the computer (her opponent) into checkmate, it doesn't even put it into check. Her bishop is on a dark square and the computer's king is on a white square.
