So...Mass effect = "the force that controls the very fabric of space and time" and mass effect relays are point to point connections that manipulate mass effect to allow space travel.
So...in order to put us in another galaxy, we need one of the dormant mass effect relays to have a twin in Andromeda. Which would be weird, unless the reapers did their cyclical harvesting thing there as well. Is this so very far-fetched? I mean, maybe they did? Maybe the original civilization that learned to harness mass effect DID travel between a few galaxies. OR, maybe one of the "jobs" of the reapers were to visit other galaxies to look for solutions to the organic-synthetic conflict (see StreetMagic's post above)? IE, instead of hibernating between cycles, they were traveling about looking for other options.
The tech issues don't seem to be a problem, in my opinion. Point is, good writers can come up with something that makes sense (can't they?).
Although...I still cringe at the whole space magic debacle...but it's all water under the bridge, neh? 
The lack continuity between the trilogy and this story is also no a problem for me, personally. I understand why some folks want to see how it all played out and all, but this is not a deal breaker for me. In fact, I think it might be a bit of a mess to incorporate the desisions in ME3. Synthesis versus Destroy is a HUGE difference, after all. I have no problems leaving all of that behind.
Plus...bring on the MAKO!! 