Okay, after going through this thread and gleaming over the many responses:
Basically, the Apple Watch is still utterly useless on WiFi without the phone close by? No notifications, no phone call information, no texts (other than iMessage), etc??? Everything is essentially cached on the phone and then pushes to the Apple Watch, once the watch is within range again?
After reading about the new update to Android Wear, what they are doing seems like true Wifi connectivity for your smartwatch. The phone and watch do not need to be on the same network and notifications come in via wifi, independent of the phone.
Maybe I am wrong??? And if I am right, then the next question is, can a software update fix the Apple Watch so it can pull info direct from the wifi connection, like Android Wear?