Okay, so to reiterate (again):
This thread is dedicated to the SYMPTOM of AirPlay Mirroring no longer functioning, specifically AFTER updating to 10.9.2. Other symptoms caused by the 10.9.2 update (such as mini displayport no longer functioning) need to have their OWN thread made.
Regarding AirParrot causing the problem AFTER the update:
Poster "Joseph Rose" above asked how AirParrot could cause a problem after updating. It seems this logic is being used all around to show that 10.9.2 is the cause of the problem, not AirParrot. However, what this does prove is that, yes, something in 10.9.2 is incompatible with the AirParrot kernel extensions that was not incompatible in previous versions of Mavericks.
Why is this AirParrot's problem?
It's AirParrot's problem because it is their job to conform to Apple's OS, not Apple's job to verify third party software will function. AirParrot needs to provide a software update in order to fix this issue and allow it to work with the latest version of Mavericks.
Now, in addition to running the commands mentioned above in Terminal:
sudo rm -rf /System/Library/Extensions/APExtFramebuffer.kext
sudo rm -rf /System/Library/Extensions/AirParrotDriver.kext
sudo rm -rf /Library/Extensions/APExtFramebuffer.kext
sudo rm -rf /Library/Extensions/AirParrotDriver.kext
Everyone should also make sure that:
1. AirParrot (if installed) is fully updated
2. All MacOS updates have been run
3. All AppleTV updates have been run.
If this issue persists after this, can someone please try resetting PRAM and SMC?
Also, if someone wants to take one for the team, can someone who is currently having the issue try installing a fresh OS, update to 10.9.2 and see if the issue persists?