Loner outsider with no real friends: Check <- Not true. He had Robb and to a lesser degree because of the age difference Bran. In the Nightwatch he has plenty of friends. Grenn, Pyp, the fat one.
His brothers like him because he has such a sparkling personality. In fact, every even vaguely sympathetic character likes him. How could they not? People who don't like Jon may as well be twirling mustachios. Lord Mormont likes him, immediately, decides to groom his as his successor after about an hour. Mance likes him, immediately, to the point of accepting the idiotic conceit that he's abandoned the NW. Aemon Targarryian like him. These aren't "real friends" however. These are people for Jon to rescue. Halfhand likes him so much he wants him to kill him. He's clearly a likable guy. Unless you're evil, of course, then you instantly hate him. This is how we can tell that Mel isn't necessarily evil, she doesn't hate Jon instantly.
Great warrior: Check <- Because he received intensive training his whole life by Ned Stark and the white bearded fellow. I don't think he's superior to Robb in that respect. And he would not stand a chance against Jaime (with both hands), the Red Viper, one of the Cleganes or someone other in their league.
No, his albino wolf would kill them at the last minute after Jon tried really hard. Starting to see the problem? Also you left out Barristan, who if you read carefully, is probably the most dangerous one on one combatant alive, even at 60+
Borderline manga style super pet: Albino dire-wolf? Really, George?: Check <- A trait he shares with all his 'siblings'. The albino part is a bit over the top but at least it makes sense stoywise.
Really? It "makes sense" story-wise? The whole dire-wolf thing makes no sense. It's an early hook to demonstrate that magic is coming back into the world. It may as well be fan fiction. It makes as much sense as the giant lions the Lannisters have, except for Tyrrion who found a dwarf one, and the 30 foot Stag that Stannis rides into battle.
Magical powers?: Check <- Shared with his siblings again. And he's not even close to Bran.
I'm not sure how "shared with his siblings" justifies stupidness. Bran's character is as comical, just incredibly boring to read. "Bran rode on Hodor's back....<20 pages of handwaive vague mythology>" Bran's story arc is clearly cribbed from one of the early drafts of "The Golden Child". Bloodraven is interesting and a deeper mythic archetype. Having to have Bran be supermagicbaby to get exposition on the BR stuff is lazy and tiring to read.
Daddy issues: Check <- Comes with being a bastard/adopted.
Yeah, not **** Daddy issues come with daddy issues? Who knew? There's no reason to have Jon be a bastard, though. I mean aside from the big "reveal" that he's Reagar's kid. That's the daddy I'm talking about.
Born leader: Check<- Again that is due to his uprising. He is not a better leader than Robb.
I assume you mean upbringing. He's clearly a better leader than Robb. Did you mean not a better general? I'm sure he'll be revealed to be. We really haven't had the opportunity to find out yet. As to the "upbringing" handwaive, Samwell, Jonas Slynt, etc have simmilar upbringings without magically being born leaders. Am I to believe that the Stark blood just magiks that up in the boys?
Wins over savages to the white man's grace by "understanding" their customs and beliefs almost instantly: Check <- Most of them don't really like him. Only the ones that know him from the time he spent with them.
Right. Of course, once they get to know they'll love him immediately. I mean, unless they're eeeevil.
Slays undead: Check <- He's not the only one. Even the fat one kills one of the Others und thus earnes his title Slayer.
You mean Sam, who kills one with the dragonglass that Jon finds and tells him to keep after Sam dismisses it as unimportant? Is that what you meant? When Jon basically saves Sams life in loco parentis with his sage advice?
He pretty much did what anyone in this position would have done. And it was enough to hold the enemy at bay long enough. Don't see a problem here.
You don't see a "problem" with Mance hanging around and being rebuffed for days as he sens small groups of forces at the wall like a Bruce Lee villain with 20 henchmen?