Most have been said, but in general I am fairly happy with the 5DIII. I have had absolutely no issues with it. In general I am easily tempted, so I suppose that will happen this time to. But to create an interest beyond just having the latest and greatest, I would want:
Significantly improved dynamic range at any ISO
Significant improvement in resolution, beyond what the 800/800E have.
Real auto ISO in manual mode, including an easily available exposure compensation function (like the one we currently have in other modes)
More intelligence in the AF system, ref. 1DX type performance, including visible AF confirmation points in low light.
Faster memory cards. I can live with having two types, but would prefer 2xCF.
Higher fps would be nice, but I will use the 1DX when speed is required anyway. To process 10fps series of 45MP images ... not fun!
Improved AF in live view would be nice, but not at the expense of resolution or DR.
Video: No requirements. If I could save $100 on a non-video body, I would probably go for that.