According to a community manager in a forum post, “While we think cross-platform play would be awesome, there are currently no plans to allow connectivity between PlayStation Network and Battle.net (this is pretty standard for most games that have PC and console support). As a result, the characters on your Battle.net account and PlayStation account will also remain separate.”
The manager also stated that gamepad support for the PC version was not planned - at least not yet.
“In terms of allowing an analog controller hookup for the PC, we don’t have any plans for that kind of support right now. Similarly, since Diablo III for console was designed with a controller in mind, the PlayStation version of Diablo III will not support USB mice or keyboards,” the manager stated.
Blizzard has yet to answer the question of whether the Real Money Auction House will be available in the console version. It seems unlikely if the console version has an offline (read as: hackable) mode.