Inconsistencies between this and Wolverine and the X-men
I've heard it being said frequently that the Wolverine short is supposed to be set in the same continuity as Wolverine and the X-men. However, there are in fact numerous inconsistencies between this short and what we see in the episodes 'Stolen Lives' and 'Past Discretions' of that series.
SPOILERS
To begin with, in this episode, Wolverine seems to remember Weapon X and recognises Sabertooth and the Professor. In WatXM however, which is set AFTER this, he doesn't remember anything about Sabertooth or Weapon X, suggesting he is encountering both for the first time since his amnesia. Furthermore, the Professor is killed in this episode and the Weapon X base where Logan received his claws destroyed...yet the Professor is alive in WatXM and the Weapon X base seems intact, only to be destroyed 'again' there. These are, to my mind, the single biggest discrepancies.
But there are others, to be sure.
In the flashbacks of this short, we see Logan being captured by force outside a bar, given the adamantium treatment, being systematically mindwiped and reprogrammed as a killing machine, and escaping during the process...all of which is pretty much a faithful adaptation of the 'Weapon X' miniseries.
However a lot of this conflicts with what we see (or can surmise) from WatXM. We see Logan working for Team X alongside Victor Creed/Sabertooth (which is also true to the comics), but he already seems to have his claws. But, as per the Hulk vs. short, Logan escaped from Weapon X just after getting his claws so there's hardly a chance he carried out any missions in the interim, at the time when he was being treated like a lab rat by the Professor as per the short. Come to think of it, if Logan's memories were wiped after the adamantium process, then how does he not remember the mission against Christopher Nord, seeing as it should have been post-amnesia if he had his claws?