I just want to add another voice to this discussion.
First of all I should mention that I work for a company that
makes high-end NAS devices (NetApp). I'd use one of their devices
but for personal use, but they're a bit out of my price range, and
probably the power requirements would blow all the circuit breakers
in my tiny apartment.

This doesn't make me an expert on all
NAS devices, and certainly not on the end of the product range that
I can afford for myself. But there are a lot of people I work with
who do know a lot about that stuff, and a lot of them use Synology
for their own home NAS purposes, and I got pretty uniformly positive
reviews of it from them. However, none of them have the unit I got.
My own experience has been frustrating like those others I read on this thread.
I also just have to hope that Synology customer support will come up with
something to get me going again.
I also recently got a DS1512+. It worked fine for a few weeks.
A week ago I found it powered down. Turns out I had set a power down
schedule that I intended to use one time the week before but forgot about it
so it kicked in a week later. OK, not a bug, just operator error *so far*.
When I tried to power it back up, I got the blue flashing light and the unit
would not come up. I fiddled around with it some, unplugged cables, etc, plugged
things back in, and it came back up and worked fine. I figured it was just operator
error and that I just didn't understand something about the power up/down behavior.
When it came back up I made sure to disable that power down schedule!
But then this week, again a week later I found it powered down again.
This time it should not have happened since I *know* I disabled the power
down schedule.
Again I tried fiddling with the cables, but this time I couldn't get past
the flashing blue light.
Something is definitely fishy and I'm pretty thoroughly annoyed.

I is not clear to me whether this is a software or firmware bug, or
a hardware problem. If it's a hardware problem, the fact that lots of others
are seeing it suggests it could be a design issue of some kind, which won't
be fixed by replacement unless the replacement has the design flaw fixed.
But, this is just conjecture since I don't really know what's wrong any
more than anybody else on this thread.