The major sticking point for most people looks to be James's lack of pace and mobility, probably because these exact qualities are lacking in the no. 10s we are trying to improve upon (Mata and Rooney). Watching him I'd say his pace is average for a no. 10, but still quicker than Rooney or Mata. His dribbling could be considered above average overall, especially in England. While he's confident enough to take on his man if he needs to, it's not really his game.
I'll add something that hasn't been said about James thus far, and that's his reluctance to use his right foot for anything but short passes. While he's no Valencia in this regard, he's very one-footed for a top player. Here's a video published when he reached 100 career goals for club and country - almost all of his goals are taken on his left foot, and he seems to score roughly the same number of goals with his head as he does with his right foot.
That said, it's one hell of a left foot. He strikes the ball very cleanly, with minimal backlift, with great accuracy and power.
Right now we don't have anyone who can really do that, which means one less thing for opposition defences to worry about (it's not like they have that much to worry about us at this point anyway). So again, having him around would improve us.
Some have called him a fair weather player and we have plenty of those - except James is even better on his day. Whether or not he'd be willing to dedicate himself to work hard for a team that doesn't have a Ronaldo to carry the team when they're having an off day, now that's open to question. I can't see him being that keen to move to England at all, which means we could end up with another Di Maria situation on our hands. I think he's talented enough to make it here if he really wanted to, but how would he respond to playing in a different league, with an inferior team?