Well, I am in the process of testing on my 1520. I noticed one thing from the start: I was not able to train easily and I wondered how come the 4 microphones on the 1520 are not working or what? Then I tried taking the phone out of its nokia case (my phone came with a nokia cover). So far, here are my observations on waking up the phone with 'Hey Cortana': 1. If the front cover is closed, the phone doesn't wake up. 2. If the front cover is open, the phone usually will wake up if its in front of me. 3. Once the phone is awake, the voice input is recognized with great accuracy, although I speak with a heavy accent. So I would say if your phone is in any kind of cover, remove it and then test hey cortana, it should improve things.
Other than that, I would really love Cortana does a few more things. For example, if I ask it to read me my text messages since I left the room, change phone settings etc.