I have been experiencing the same issue, not only with my Apple Watch Series 1, but with the Series 2 that arrived yesterday. I have restored my iPhone with a fresh iOS 10 in DFU. The watch was cleared and I have setup both and brand new with no restore from backup. I am interested in others experience but I did note, I use an apple ID that was once a .mac was then a .me and now a .icloud...... When I sign in to a device I usually use .me as I have had the habit the longest, but when I review any settings that use my apple ID it represents itself as .mac, so I tried (after another restore) to setup all my devices with .mac at login rather than .me, it did not fix the issue, but curiously when people would invite me using .icloud or .me or even my phone number I would get the invite, accept and then get a spinning cog, but if anyone invited me using .mac they would get an error saying the person needs to have an apple watch to share activity. I am getting the feeling this may at times be an issue with the apple ID? Does anyone else use legacy .mac or .me who are having this issue?