I actually saw the film last Thursday but didn't get around to writing a review. As a long time Wolverine fan and someone who thinks his Japanese arc is one of the best comics ever written, I was very happy with the movie.
I liked how the film took it's time, showing us how down Logan was, then the story developed with Yashida, Logan taking in the Japanese culture (Mangold created a great atmosphere) and especially the relationships between him, Yukio and Mariko, they gave the film it's heart and invested me in the action once s**t hit the fan.
Speaking of the action, I loved the chase sequence as Logan tried to protect Mariko from the Yakuza as Harada picked them off from above, one zoom shot in particular was fantastic. Then there was the Bullet Train sequence which I thought was brilliant.
My favourite part of the movie followed said sequence with Logan and Mariko in the small fishing village, the way she helped Logan find some peace was beautifully done, Tao Okamoto was perfect as Mariko, a serene mix of strength, beauty and gentleness.
Amidst the drama and action the film also had a sharp sense of humour, something best showcased in the scene where Logan and Yukio go to see Noburo.

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I liked that Shingen and Yashida had different motives, it made the story more interesting and the fight between Wolverine and Shingen was badass, whilst Viper was creepy as hell and served to feed in the mutant element.
The finale was not quite what I hoped for, at least from an execution standpoint. I was happy enough but the heavily cut Ninja battle was disappointing and while I felt the Robo-Samurai suit worked from a narrative perspective, it didn't provide a great fight scene.
The way the film ended with Mariko and Logan still connected makes me hope that Wolverine will end up in Japan again, and I loved the final scene of him and Yukio on the plane with her now anointing herself as his bodyguard!
8.5/10