Well, as joe and Jim have said, it is difficult to help without a little more information. First of all, congratulations on getting the 5D Mark III. I researched it yesterday after a discussion about bit rates. If you are using the all I-Frame setting, you should be getting some very good video, assuming all of the correct composition, lighting, settings, etc.
What I can tell you is that the Vimeo preset uses 5Mb/s whereas the YouTube preset uses 8Mb/s. That can be significant with some footage, and not so much with other footage. So I suppose the first question is: are you using Vimeo?
I have done extensive research on the difference between my camera's video and photographs scaled to the same frame size and the video is not bad. I had the assistance of one of the smartest video guys I know so I am confident of the analysis.
Not great, but not bad. And the problems require about a 300% zoom to really analyze them. But that is not your issue. You want to see your video exported as clean as it was imported. That isn't possible, but you might be able to get closer if you post a few seconds of video that you want to export, and then post the export, along with a screen shot of your settings (unless you are truly using the default). Then we can all try it and see what happens.
You might want to shoot 10 seconds of something with no motion at all. Then 10 seconds of a lot of motion. It would make for a better analysis. Shoot it specifically for this test. Have some text in the shot from a box or a sign, or some other sharp lines.