It's bound to happen. With new gear comes new bugs and Canon Rumors has already reported on the first two issues with Canon's 5D MarkIII.
Image Stabilization Noise
A couple of lenses have been exhibiting strange noises when the shutter button is half depressed on the 5d MarkIII but the image quality is not affected and the noise does not occur during Live View. The two known affected lenses are the Canon EF 200mm f/2.0 L IS USM Lens and the Canon EF 800mm f/5.6 L IS USM Lens.
Canon USA has issued an official response to the 5D III IS noise issue: “We have acknowledged that when using the camera with specific lenses, there is an abnormal noise during IS operation when the shutter button is pressed halfway (or remains pressed halfway), and we are now considering the countermeasures. We will let you know about the countermeasures as soon as they are finalized”
Low Shutter Sync Speeds
Apparently the 5D MarkIII won’t sync at shutter speeds higher than 1/160 using Pocket Wizard's Mini TT1 with some lighting set ups.
Pocket Wizard's response to the low shutter sync speeds issue:"...they say it’s not compatible yet and although the 5D III should sync at at least 1/200, the actual speed of the shutter is lower (approx 1/160). They don’t even have a test camera yet and they expect the soon-to-be-released 1D X not to be compatible either. They will be working on a firmware update as soon as they have a 5D MarkIII to work with."
All in all, the reviews on the 5D MarkIII have been good and we are bound to see some growing pains. Still, I can't help but feel that the Nikon D800 camp seems to be fairing a bit better though.