Updated to Mavericks as well from Mountain Lion....
I have spent most of this afternoon working on the signin issue with facetime and iMessage with Apple support. We have tried many of the recommendations like reset NVPRAM, making sure your time zone / time is correct on mac, create new user, removing NetworkInterfaces.plist, removing iCloud account and turning it on again, safemode, reinstall Mavericks over top again, changing apple ID password, deleting key chain enteries, etc.... the list goes on. Nothing has helped. FYI my account works fine on my other macs, just not my MBP. Weird.
I would be interested if anyone can look at their system.log and get a snippet of the log when you try to log in. Mine looks like this:
10-24-2013 8:09:47.232 PM FaceTime[587]: Retrieving server bag 1, 0x600000014990, 0, 0
10-24-2013 8:09:51.917 PM com.apple.SecurityServer[14]: Session 100029 created
10-24-2013 8:09:51.980 PM apsd[108]: Certificate doesn't match host
10-24-2013 8:09:51.980 PM apsd[108]: Stored identifier doesn't match host
10-24-2013 8:09:51.981 PM apsd[108]: Stored identifier doesn't match host
10-24-2013 8:09:51.981 PM apsd[108]: Certificate doesn't match host
10-24-2013 8:09:51.987 PM apsd[108]: Certificate doesn't match host
10-24-2013 8:09:54.740 PM FaceTime[587]: Retrieving server bag 1, 0x600000014990, 1, 0
10-24-2013 8:10:51.978 PM apsd[108]: Certificate doesn't match host
10-24-2013 8:10:51.978 PM apsd[108]: Stored identifier doesn't match host
10-24-2013 8:10:51.978 PM apsd[108]: Stored identifier doesn't match host
10-24-2013 8:10:51.978 PM apsd[108]: Certificate doesn't match host
10-24-2013 8:10:51.980 PM apsd[108]: Certificate doesn't match host
10-24-2013 8:10:51.982 PM apsd[108]: Certificate doesn't match host
10-24-2013 8:10:52.035 PM identityservicesd[454]: [Warning] Tried to disable an account we don't know about, ignoring...
My next step is to backup my data and do a clean install.... I am hoping there is a fix before I pull the pin and do this.