When Mikhail begins fighting with Sayid and Kate, his nose starts bleeding before he is hit there.
When Sayid points a Mosin Nagant 91/30 rifle at Ms Klugh, the bolt of the rifle alternates between the locked (ready to fire) and open/unlocked position. Not only is this a continuity error, but if fired in this unlocked position, the results would be a catastrophic failure of the rifle.
When John beats the computer in a chess game, the computer flashes the message "CHECKMATE", then "YOU WIN." The position on the board is not a checkmate, although John has a forced mate in two.
When Mikhail shoots Sayid, the rifle is on his right side, however, he also wears an eye patch on his right eye, which would make it impossible for him to shoot from that side.