According to BioWare:
2) Is constant Origin connection required or is it a single one off authentication when the game is first installed. Is there also a limit to the number of installations available?
Mass Effect 3 will require a one time, single authorization for the single player game. There is no limit to the number of installs. Playing Mass Effect 3 Multiplayer will require a constant connection.
I believe this was intended for the PC version, but PS3/Xbox 360 DRM tends to be less strict than its PC counterparts, so I'd say it's unlikely that the PS3 will require a constant connection for single player.
When you start the game on consoles, you get the following message:
Welcome to EA Servers.
You must create an Origin Account (EA) or log in to an existing one to join multiplayer games or access online features.
I was given the option to cancel, and even if I did, I could still play the single player campaign. Therefore, I don't believe that there's always-on DRM for consoles for this title.
However, the game seems to authenticate with EA servers every time you load - it appears as though DLC installed alongside the game may be checked at each load. Some users are reporting that they are locked out of their DLC if the game is unable to authenticate with EA servers. Bioware has not released anything official on this matter, and all I have are sporadic reports on forums that seem to be talking mainly about the PC.