I had this problem on OSX and found this thread. It helped a lot, and I was able to fix the problem, but it wasn't super clear, and I thought I'd explain what I'd learned along the way.
Here's how I think I got to have the problem:
In Facetime preferences (Start the Facetime App, choose Facetime | Preferences from the menu), there's an checkbox labeled "Calls from iPhone". In the past, that box was checked. I think it was a default, though it's possible I checked it and don't remember. When that box was checked, every time I got a phone call on my iPhone, Facetime would start on my Mac and start ringing. I found that behavior annoying, so I unchecked the box. Great. No more phone ringing on my Mac. But, when I unchecked the box, I had a lot of missed calls logged on Facetime, because of all the calls that were routed through from my iPhone.
The badge count (the number in the red circle that appears on the Facetime icon in the dock) shows the number of missed calls that the user has yet to view in the Facetime app. And unchecking that box in Preferences hides all the calls that came from the iPhone when the box was checked. So I had a lot of missed calls that I had yet to view (hence the badge) and no way to view them, as with the box unchecked they were hidden.
Solution:
- Recheck "Calls from iPhone" in Facetime preferences
- Activate the main Facetime window and make sure Audio is chosen from the Audio/Video chooser.
- At this point, the badge count should disappear, as you've viewed those missed calls that were previously hidden. No need to click on them or anything; just having them displayed on the screen counts as viewing.
- Return to Facetime preferences and uncheck the "Calls from iPhone" box