I'm not sure if this will help, because it looks like people have various symptoms associated with this problem, but I had the issue of alarms not going off when I upgraded to the Moto X 2014 (never had the problem with my 2013 model). I noticed the first time I used the alarm clock, I did not hear the alarm go off (luckily I am paranoid and always set a real alarm clock as a backup), but when I woke up my phone showed a notification about a missed alarm. I tried a bunch of things and here's what worked:
My alarm is supposed to go off at 6:15AM, I had Moto Assist set to sleep mode from 11PM - 7AM, so that I could have coffee and time to wake up before my phone starts ringing. I think that the new way Lollipop handles "interruptions" was causing my alarm to be silenced as well as notifications. I changed the sleep mode hours to 11PM-6AM and I haven't had any problems with my alarm since then.
Like I said, it seems that some people are having this issue even without setting up Moto Assist, so I'm not sure if this helps, but at least in my case, I think it has something to do with the "interruptions" setting, and the phone being set to mute while "Sleep" mode is active.