BioWare has tweeted that a Mass Effect 3 singleplayer demo and multiplayer early access beta will be hitting the unsuspecting galaxy in January 2012. Firm dates will be finalised next month, but for now, be aware that owners of Battlefield 3 (and the Online Pass if you don't buy it on Origin, natch), will automatically gain early access to the Mass Effect 3 demo via their EA Account. Apparently an online tool will soon be available to check your eligibility.
I may or may not have tried out the multiplayer - and may or may not be able to tell you about it in six days' time. Embargoes are fun.