Wolverine as a character, across all Marvel media, is defined by two physical and two emotional attributes. He has claws, and he heals quickly. He has a temper, and he loves Jean Grey. He is notable in Marvel history for being a hero willing to kill. This was a very big deal at the time - modern heroes, and modern versions of classic heroes, don't have as much trouble killing, but back in the day a Marvel hero would avoid killing anyone for any reason.
I bring this up because The Wolverine (the movie) is at its core about mortality, illustrated in contrasting extremes in the persons of Wolverine and Yashida. The former, depressed over the loss of Jean, begins the movie tired of life, but his healing factor gives him something approaching immortality. The latter begins the movie in the final stages of terminal illness. The relationship between these two drives the plot, and there are some nice, if not terribly deep, statements about what it means to be alive.
The film also deals nicely with Wolverine's emotional side. In X-Men: The Last Stand, Wolverine was forced to kill Jean in order to stop the Phoenix. The parts of the movie not taken up by action sequences or the mortality plot arc involve Wolverine dealing (or failing to deal) with Jean's death, while at the same time dealing with a possible new love interest.
These are solid story elements, and they could have - maybe should have - resulted in a great film. Instead, they resulted in an okay film. It took me a while to realize why. The film has no joy. There is no witty banter, no humor, no fun. There is only one moment that really has the dark humor that the movie needs, and while it's a good one, it isn't enough.
Action movies don't always need humor, of course. Unfortunately, the action sequences aren't that great either. They aren't bad - with the exception of several chase sequences that are more or less unwatchable due to shakycam - but they aren't inspired.
The acting is generally decent. Rila Fukushima, who plays Yukio, is the weakest of the main cast, which is a shame because she gets a lot of screen time. Hugh Jackman did a fine job with the title role, as usual. I am eternally impressed that a man who has two Tony awards can also headline a superhero action franchise.
As a final quibble, there are a couple points in the film where characters display knowledge of events which they have no demonstrated way of knowing.
If you do see this movie, stick around past the first part of the credits. There is a bit of set-up for X-Men: Days of Future Past.
1. Much Ado About Nothing
2. Now You See Me
3. Despicable Me 2
4. Star Trek: Into Darkness
6. Iron Man 3
7. Man of Steel
8. Pacific Rim
9. Jack the Giant Slayer
10. Beautiful Creatures
12. Oz the Great and Powerful
14. G.I. Joe: Retaliation
15. The Wolverine
16. Monsters University
17. Hansel and Gretel, Witch Hunters
18. The Great Gatsby
19. The Lone Ranger
20. This is the End