The Wolverine starts with the eponymous protagonist's encounter with Yashida during World War II. This does clearly happen before the events of X-Men Origins: Wolverine, during which he completely loses his memory, which is also a major plot element of the X-Men trilogy. Yet, in the most recent events in The Wolverine he can clearly remember Yashida and their experiences back then.
Now I know that there are other significant and yet to be resolved (or not) continuity problems between the different X-Men franchises, so maybe this is just one of them. But it may very well be that I just missed something in the story of the movies or this is explained elsewhere (maybe he suddenly got all his memories back when he remembered Striker's experiment in X2?). So is there any information why Logan is able to remember Yashida from before his amnesia?