USB audio problems with 2013 iMac

Question

I'm having a strange audio problem with USB microphones and headsets. The issue with my Logitech H650e is shown in this screencast I recorded. In the first part of the screencast, I am not speaking into the mic—yet you can see the levels fluctuating as if there is static playing (not in a natural pattern that you'd see when someone is speaking). In the next part of the video I demonstrate that selecting the built-in iMac mic for input, and then re-selecting the Logitech headset temporarily solves the problem. You can see the input start to fluctuate normally as it should when I am speaking. But at 0:31 in the screencast, you can see the input levels freeze and stop registering anything. I continued to speak until the end of the screencast, but no input was detected. For this screencast, I was on a Go To Webinar call, but the problem occurs regardless of whether I'm using Skype, Go To Webinar, GarageBand or any other software.
The problem with my Blue Yeti USB microphone is also different. In that case, the input does not freeze as it does with the Logitech headset. The levels appear as you would expect, and it seems to work. However, the person on the other end can hear static in the background, even though I don't hear it in my own headphones. I learned this because I just tried to do a Skype interview with the Blue Yeti, and the interviewer told me they could hear static. We closed Skype and called each other back twice, but the problem persisted. Then, suspecting the problem was related to what I described above with the Logitech, I unplugged the Yeti and then plugged it into my Macbook Air 2013 (also running Mavericks). Lo and behold the static completely disappeared.
My Griffin iMic and Audio Technica lavalier mic (attached to the iMic) behaves similarly to the Yeti, except in this case I can hear the static when I speak with my monitoring headphones. The input works but I get a lot of cracking and static in the background. This was confirmed by calling the Skype Test Call number and recording a message, which is then played back.
Here are the facts:
All 3 of my USB audio microphones/headsets do not work with my 2013 iMac running Mavericks
All 3 of these microphones/headsets worked fine with my 2008 Mac Pro running Mountain Lion
All 3 of these microphones/headsets work fine with my 2013 Macbook Air running Mavericks
In this other thread, several people are reporting similar issues with the iMac 2013 and Mavericks. At least two people did not have the issue when the iMac 2013 was running Mountain Lion. This of course suggests the issue is the combination of the iMac 2013 and Mavericks. 

Answer 1

Apple>About This Mac>More Info>Service
Please read the warranty paperwork that came w/your computer.
You have 14 days to return the computer w/no questions asked. 
You have 90 days of FREE phone tech support on top of your standard 1 year warranty unless you also purchased AppleCare which gives you an additional 2 years of coverage plus FREE phone support.
Strongly suggest that you take FULL advantage of the above before it runs out.  Let Apple deal w/the problems.