I may have discovered the source of my problem. The early 2013 MacBook Retina has 802.11n. This feature requires 802.11ac. It's a $30 part on Amazon. I've ordered it and it will be here in two days. All reports are that this will solve my problem. I'll talk to the Apple engineers before switching it out however.
If this is all true, Apple needs to far more clear about compatibility. It may not simply be 2013 or newer, but those which also have the AC wireless cards.
Pretty sure they said "late 2013" did they not?
BLE and 802.11AC are required for the feature. (that's been known for some time due to the beta program).
It's very temperamental in many cases to get it working, however, there's lots of checks in your iCloud settings that often require toggling many of the settings (handoff, iCloud, messenger, FaceTime).
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Even if this does fix that part of the problem for me, I cannot get my watch, which I only got yesterday, to stay connected to my phone via bluetooth. It constantly disconnects.
Best of luck to you though. I'll report back with whatever I hear from Apple.
At least the original Apple Watch had a very weak Bluetooth radio. (not sure how much it's been improved for S1 & S2).
You should certainly have at least 20-30 feet (line of sight) between the watch and iPhone.
The watch switches over to wifi when the bluetooth connection is lost (when you do the initial setup, you should have your iPhone on a 2.4GHz network, as the watch wants to be on the same network as the iPhone but doesn't have a 5GHz radio).