Battery drain on the phone!
For me this is the main Achilles heel of the watch. I have a Nexus 5 which by todays standards has reasonable battery life, however, paired with the SW2, it will not last a day.
Now my understanding is that the main culprit is the Bluetooth used on the SW2 is causing the main drain. This makes sense to me, as surely the processing required by the phone is minimal and it's the screen that consumes much of the battery.... and that every other BT device I've connected has similar consequences.
The big advantage of the LG G Watch whilst I used it, was that whilst the watch only just lasted a day, the impact on the phone was the opposite. Instead of having to look at the phone for every alert, I looked at the watch. The result was that the phone battery consumption improved.
From what I have read, this is more to do with the battery 'sipping' BlueTooth 4.