1) The game requires a constant internet connection. It cannot be played offline.
2) Mods are "expressly prohibited."
3) Items in the auction house are bought and sold for real-life money.
In order, here's Blizzard's justifications:
1) "One of the things that we felt was really important was that if you did play offline, if we allowed for that experience, you'd start a character, you'd get him all the way to level 20 or level 30 or level 40 or what have you, and then at that point you might decide to want to venture onto Battle.net. But you'd have to start a character from scratch, because there'd be no way for us to guarantee no cheats were involved, if we let you play on the client and then take that character online." Also, piracy.
3) "We think it's really going to add a lot of depth to the game. If I have more money than time I can purchase items, or if I'm leet in the game I can get benefits out of it. The players really want it. This is something that we know people are going to do either way. We can provide them a really safe, awesome, fun experience, or they'll find ways of doing it elsewhere." Blizzard will take a small cut, but they're not expecting to make too much of a profit out of it themselves. They also say there'll be level caps on items, so you can't immediately shortcut to a high-level sword with a level-1 character, not matter how rich you are, plus there will also be an additional auction house that uses in-game gold. So this element of the game can, at least, be dodged entirely.