Well I decided to rent the Canon 6D and shot with it at a car show today using my old 28-80 L lenses. Wow, did the pictures stink! Vignetting on almost all the pictures and none of the images were really "sharp". I have the camera until Monday and will continue to test it with my other lenses on Sunday.
I was really hoping I wouldn't have to replace my 28-80 L with a newer L lens. It's great on a APS-C body but is horrible on a FF camera.
Are you shooting jpeg? If so, there might be a lens profile you could install on the camera to sort out vignetting and CA. Use the free Canon EOS utility, plugged into the camera to update it. If you're shooting raw, try the same automatic lens correction in LR or whatever you're using. It might well tidy it up quite bit.
Also remember to feel free to stop it down about one a third stops beyond what you'd use on crop - that way you maintain the same DoF, and the lower noise levels of the FF sensor will allow you to boost the ISO to shoot in the same low light situations (or even darker). Stopping it down will reduce these issues you've noticed. If you want to open it up, just remember you're in territory that the crop camera couldn't go to.