Revealing mistake: In the beginning of the movie when Wolverine puts the cigar out in his hand, you can see the mark of a wedding ring on his ring finger (Hugh Jackman is married). Even if Wolverine got married during the "blurred" bit of his memory so doesn't remember it (tenuous at best), his healing ability would have removed any ring mark. Either way it just doesn't belong.
Picture added by Cochrane
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