I suspect they'll have a good season domestically and come somewhat undone in Europe (unless they drop to the Europa League).
They're going to punch, kick and grind their way through a lot of games next season. They showed signs of it in the 2nd half of last season, and with a full preseason with a more "Mourinho" squad (assuming more similar players come in too) I imagine they will win most games in a rather ugly fashion. But most games nonetheless, a bit like they did in 2010/11.
It's not nice on the eye but focusing on the physical element is clever enough. I still maintain Monaco beat us through strength and force. Spurs did it to everyone but us and Liverpool last season and I hate to say it but the best United teams of old had a hugely physical element.
Sure, they can't play pretty football for shit, which I think will be their undoing abroad; but in England where you can get by without being 'good' they could thrive.
One big problem they though is the lack of natural wingers who are any good (ie not Young). They play with wide attackers which cuts off some, but plenty, of the aerial supply to the bigman up front. What's weird though is they don't at least have any top quality fullbacks to compensate for it. It goes against the hoofball type. So naturally I'd be concerned more if they got a decent winger (or a really good fullback) as opposed to a James kind of player. That'd tell me they're thinking coherently, which up to now they fortunately have not.
I don't look forward to watching them play next season, that's for sure :P