What's with the number in a red circle above the Facetime icon in the dock?

Settings > Notifications > FaceTime > Badge App Icon OFF.

I have that problem also. How to get of the red circle with the number?

When all call are deleted it still remains.

I'm interested in this too, kongakut2012. I can't see an envelope either. I discovered that the number probably meant that I had a missed call, but when I cleared all recent calls (including the missed one) the number didn't go away. So -- where's the envelope, please???

It means you have an invitation to an event !!! Click on the envelope to get a choice of what to do.

The flag on the FaceTime app is the number of missed calls.

Do a hard reset. That red circle was driving me nuts too! That fixed it for me, after checking every darn button on Facetime and having no luck.

I am running Lion still... I right clicked and did 'show recents'... and it went away.....

Under Lion and Mountain Lion. there's a RECENTS button in the bottom right corner of Facetime main window. Click it, then there's a list of recents (similar to iOS) and a Clear button.

Try opening FaceTime and tick the "Calls from Phone" box, then untick it.

I had it stuck on 1 notification and this fixed it as it must have synced with my phone again.

Thank you. GSP in Oregon