I've been running the Lollipop developer previews for a while (on a Nexus 5), with no Android Wear issues, but now that I've upgraded to "Stock" Lollipop I'm not getting Hangouts or Inbox notifications sent to my Moto360. Other applications sync fine (Google Fit, Weather, Stocks, etc) but Hangouts and Inbox do not work. My phone is also not set into Priority Mode when paired to the watch anymore, like it was on Developer Builds.
Anyone else noticing these issues? Kind of defeats the purpose of the watch if I'm not getting notifications sent to it :/.
Edit: I managed to fix my problem by resetting my Moto360 and uninstalling the Android Wear application. Not sure if that was strictly necessary or not, but it seems to have done the trick, for now at least.