I haven't checked into the different modes that D3 was offering. I've only played the stress beta, and obviously that required you to be online.
Honestly I thought they did it like the way in D2, where you had Open and Closed games. Closed games was exclusively multiplayer online. It saved your character on the B.net server, and this should have made it cheat-proof (but didn't). Open games on the other hand saved your characters on your local computer. This was the option for those players that couldn't be online all the time, and I used to play that back in the day, as I didn't want huge phone bills. The downside was that it was really easy to cheat in.
I thought they would go with the same flow for D3, except that you'd probably had to log in once after installation, just like you had to do with SC2, to activate it. I wasn't aware you had to be online constantly. I guess Blizzard is thinking, we're 12 years ahead, everyone has broadband nowadays.
It doesn't really affect me, since I would've only played online anyhow, but I can see it being a problem if you either don't have a permanent internet connection, or want a pause feature (Alt-Tab really doesn't do anything in multiplayer games, since the game is essentially played on the server).
As for the game itself, it's a little more colorful, less grimmy looking than it's predecessors, but that might of course just be the first part of the game. I don't regret the loss of raising your own attributes (which in the end came down to, do I want more survivability or more damage output, and if you go for damage output, and get some guys that specced almost entirely survivability in a multiplayer game, it was *yawn*). The loss of raising your own skillpoints strikes me as a tad peculiar, though. The deviation between characters are now "What skills/runes do you place on your hotbar?", rather than "What skill points did you pick?" At higher level, you'll be forced to choose among which passive skills you want to use as well, but you can easily swap between them. It feels a little eased down, but we'll see.
Oh, and you can hold your LMB to attack repeatedly. It also automatically picks up all the gold you walk over, so there's less mindless clicking involved. Also, each class has a few basic strikes that raise energy, rather than lower it, which replaces mana pots altogether.
The thing I really do regret is the hireling abandoning you the moment there are 2 players in the game.
