So I'd claim that City are the side that have the fewest number of visible weaknesses. That doesn't mean a stroll to another title: while they do have one under their belt now, and that matters, they could get distracted by other competitions, and I'm not sure they have adequate cover for an extended loss, or loss of form, of/by Yaya or Silva. And there are still questions if there's quite the necessary depth on the back line.
United don't seem to have done anything to solve the crucial creative central midfield issue. They seem to have decided against the now-popular lock-down holding midfielder type, but the way they play the position still doesn't have a natural incumbent. Also, they've spent chunks of the last two seasons hurt by injuries on the back line for which there doesn't seem to be any new protection either. They've got some interesting problems up top as well; is Nani an all-time big-time player, or is he going to be a player who make an impact in spurts? Chicharito has undeniable talents but like Suarez he seems to need to be one of a forward pairing to be effective, not a lone striker, or an attacking wide player: the role Cassani played for Italy in the Euros seems the one, but somehow it's not the fashion now to play with two strikers. United actually still do it sometimes.
Chelsea are odd, some pundits think they're in a holding pattern until they can bring in Guardiola after he recharges his batteries. They're a defensive-first side who don't have a good defense now: there's no right back; Terry has great heart and you'd never bet against him in one key match, but is not solid enough consistently any more; Luiz is still flaky; and Cahill is a bit unknown. And there's not a perfect answer for the holding midfielder for a side that tries to play one. Mikel has zero offense and is a bit erratic; whether Essien, who would be the answer off his beast form of several years ago, can ever be effective again is unknown; and we didn't get to know Romeu yet. Forward story unclear; impact of new players remains to be seen.
Arsenal have had bad starts over the past few years, they may be unsettled again over the Van Persie saga and now the Song rumors, and they've got no cover on defense - last year the lack of Vermaelen, esp. when any other front line defender was absent, was deadly. Unless something evolves, doesn't look like better than 4th is in the cards. Loss of RVP would not help, that looks unlikely now.
Liverpool will be adjusting to a new style which will probably make them better in the long run; I don't expect great things for the first half of the season. There are probably players there who need to be moved out, and questions about the back line - Agger + Skrtel is not bad, but both have to prove they can be full-season players, with histories of injury and/or discipline problems not far enough behind them yet - plus rumors one or the other could go. Still seems like no more than 5th-7th.
Newcastle... I don't know enough about them to comment at the moment. They've got good players but you get a sense of overacheivement from last season unless they manage to keep strengthening, and Pardew has already noted how the problem has gotten a lot harder, they snuck up on some people with transfers last season, but it's not happening now.
Spurs seem to understand that they have to refresh in a few areas - guess what, defense again, they were in trouble when Ledley King didn't play, which he could barely do, and has now retired - but they don't look like a club headed in the right direction at the moment. Expect somewhere 5th-7th, or maybe worse - a lot depends on AVB as there seem to already be unsettled key players and he wasn't brilliant dealing with that at at Chelsea, if it doesn't click they could drop to 10th or something.
Looking back over what I scribbled, just about every side has questions, all have back line issues, depth if nothing else, and whether players not yet proven will make the step up to prime-time contributors. Some seasons a big injury makes a difference in the overall results, it smells like one of those.
Of course, there's still time in the transfer window and some of the perceived weaknesses could end up plugged.