User 1 = MacBook Pro 15" (Late 2008), 8 GB RAM, 500 GB HD, Yosemite 10.10.1, iPhone 5s, 16 GB, iOS 8.1.2.
User 2 = MacBook Pro 13" (Early 2011), 8 GB RAM, 500 GB HDD, Yosemite 10.10.1, iPhone 5, 16 GB, iOS 8.1.2.
All 4 devices connected to same WiFi network using Apple Airport Extreme base station and Airport Express (as network extender) on cable internet conection.
User 1 = MacBook Pro 15" (FaceTime works) + iPhone 5s (FaceTime works) using same Apple ID #1.
User 2 = MacBook Pro 13" (FaceTime CLICKS) + iPhone 5 (FaceTime works) using same Apple ID #2.
FaceTime on both computers and both iPhones working fine prior to 10.10. FaceTime on the 13" (Early 2011) has the "FaceTime strange clicking sound" running Yosemite 10.10, while FaceTime on the 15" (Late 2008) works fine. This was puzzling since everything else was working fine (tested by recording audio in Quicktime Player on 13" and it had no audio clicking). Rebooted the 13", checked everything, sound input sources, read all the other "fixes" on this discussion to no avail.
After much thought and testing different combinations of hardware, software, settings, etc..., I remembered that the MacBook Pro 13" (Early 2011) has almost enough hardware to support Handoff in Yosemite 10.10. However it has Bluetooth 2.1, while Handoff requires Bluetooth 4.0. What was one of the new features in OS 10.10 that didn't exist in 10.9 or earlier when FaceTime worked fine? Handoff!!!
The solution that has fixed the FaceTime audio clicking for the user with the MacBook Pro 13" and iPhone 5 using the same Apple ID, is turning off Handoff on their iPhone 5. In iOS 8.1.2 Handoff is located under Settings / General / Handoff & Suggested Apps / Handoff - slide to OFF.
In this case I suspect there is a conflict between the iPhone 5 trying to use Handoff with the MacBook Pro 13" (Early 2011) when they are joined to the same WiFi network and using the same Apple ID. Even though the MacBook Pro 13" (Early 2011) is not supposed to be compatible with Handoff, I believe it was attempting to interact with the iPhone 5 when both were on the same WiFi network and sharing the same Apple ID #2, and this was the cause of the problem.
What is interesting, is the iPhone 5s with Handoff turned on was not causing issues with the MacBook Pro 13" or 15" all on the same WiFi network. The 15" uses the same Apple ID #1 as the iPhone 5s (Apple ID #1) but is too old (Late 2008), and the 13" is using a different (Apple ID #2). So it doesn't appear to be problem with all Handoff traffic on the network. It was the combination of the 13" MacBook Pro (Early 2011) using Apple ID #2 + iPhone 5 using Apple ID #2 with Handoff turned on + same WiFi network that caused the FaceTime clicking issue for this 13" MacBook Pro (Early 2011) user.
By turning off Handoff on the iPhone 5, we are able to use FaceTime on the MacBook Pro 13" (Early 2011) without any problems and they both share the same Apple ID #2. We were not using the Handoff feature anyways (since we didn't have 2 compatible devices on the same Apple ID) so we don't miss it. Everything appears to be working good again with all 4 devices joined to the same WiFi network.
If you have a MacBook Pro 13" with the FaceTime audio clicking with Yosemite 10.10, make sure to turn Handoff OFF on ALL of your iOS devices using the SAME Apple ID on the SAME WiFi network (i.e all your iPhone's, iPad's, etc...) and then restart your MacBook Pro and check to see if FaceTime works.
Hopefully someone else finds this information useful.