I have Battlefield 3 for PC and Mass Effect 3 for Xbox 360. I'm signed with the same account on Origin, but I can't get the Battlefield 3 multiplayer skin for Mass Effect 3 (though I have the N7 dogtag for Battlefield 3). Is this as it is supposed to be, or do I have to do something else to receive the reward?
Yes, both online passes must be redeemed on the same platform.
That would be PC+PC or 360+360, as the skin isn't available for PS3.