In response to the OP's original question, I would suggest checking a couple of things. I had to return my 5D3 after just a couple of days because it had two faults:
Hot pixels: Take a photo of something middle-grey in RAW format, then copy it to your computer and examine the whole image carefully for any bright red pixels. In my case, no amount of auto sensor cleaning made any difference whatsoever to this fault. It wasn't a single pixel either, but a cluster.
Autofocus: For the purpose of this test, choose the centre focus point and set your aperture to its widest (f/4 on the kit lens). In good lighting conditions, take a photo of something that has lines in it - something that you'll be able to easily see whether it's sharp or not. Then check for focus (at the centre of the frame, since the outer parts of the frame will be slightly out of focus anyway) on your computer. Some variation in lens calibrations is to be expected, but if, like me, you're having to set your 5D3's AF microadjustment to +20 to get things in focus, you probably have a problem.
After receiving my replacement 5D3, both of the above problems were eliminated - much to my relief!
Thank you for the great advice!!
Just curious...what series number was your 5D3 replacement? Mine is a "3".