Continuity mistake: As Wolverine bids farewell to Mariko in the next to final scene on the airport tarmac, Yukio is visible in the background of the shot standing at the foot of the stairs, where she receives a green box which she tucks under her arm. The scene cuts to Mariko, when it moves back to Wolverine, Yukio remains in the background but the green box has disappeared.
Other mistake: Wolverine shields Yashida from the blast, burning off all his hair. Somehow his pants manage to remain unaffected by this, as seen later when they are climbing from the pit.
Continuity mistake: When Mariko and Logan are eating, Logan uses a fork and leaves his chopsticks sticking straight up out of the bowl. Mariko removes them and lies them flat, saying it's bad luck. Then they keep talking and suddenly the chopsticks are vertical again without him touching them.
Continuity mistake: Just as Logan and Mariko are about to enter the room at the "love hotel", the door opposite their room shows a teddy bear on the door, but when it switches to the view from inside their room the opposite door now shows a stethoscope.
Suggested correction: They're two different doors and the teddy bear room isn't opposite their room. The teddy bear room is #30 and the stethoscope room is #31.