What psychological issues has Wolverine's difficult life has left him with? I would prefer if they were explained using modern psychological definitions and techniques.
Off the cuff (degree in Psychology) I would say he has anger management issues which could be both emotionally as well as physiologically based (chemical imbalance due to mutant nature - only blood tests could tell). Psychologically speaking watching one's father murdered in front of you could have traumatizing effects that might never get worked out. Rage, betrayal, depression - all could set in.
Intriguing that Wolverine goes on to become one of the more Zen characters later in life - the kinds of neuroses and personality disorders (not including flirting with sociopathic rage, which he fortunately has enough of a moral identity to barely avoid - i.e. randomly killing innocents) often dictate devotion to some kind (any kind) of spiritual belief as a pathway towards what is called "Recovery" (i.e. a normal life...ish). Zen in particular is very centered around calming the mind from any and all turbulence, so the fact that Wolverine steadies himself by way of Zen is a pretty great statement that he is on a serious path of Recovery.
In addition, growing up without a father also leads to classic symptoms ranging from incredibly "spoiled" (I get what I want) to an excessive need to prove oneself to the ideal of a father inside. Its quite possible that the reason the relatively untamable Wolverine is so loyal to the Xmen is (at least partially) that Xavier is his surrogate father figure. This would be validated by gestures Wolverine makes to win Xavier's approval any time it seems like he is trying too hard.
Again thats just off the top of my head. :)