If you have not changed the setting, the images are saved in the best quality.
What settings and lens do you use (aperture, shutter speed etc.)? Handheld ord not?
It´s a fact that the images you see through the viewfinder are much sharper and better than the images saved as JPG. The JPG-image quality from the 5D Mark III are in my opinion unusable and a big step worser then the JPG-images from the 5D Mark II or 1Ds Mark III (only from ISO 50 to ISO 800).