Without any bashing or being a Canon fan, give Reikan FoCal a try.
AFMA is there for a reason and so that you wouldn't have to (necessarily) send your gear to Canon for focus adjustment. The reason behind all this being of course the tolerances in manufacturing.
With your MkIV and lenses you might have been lucky and the tolerances have been 0/0 or so small that they don't matter within the DOF. You instantly get bigger problems if say your MkIV has been -3 and your lenses (for arguments sake) from +2 to +4, but your MkIII is +4 so the problem is really visible now.
If the focus adjustment is off, there's no setting in the AF- menu that will make your photos sharper.
Just my 0.02$
Can people please read the post in see that it is shot in LV=LIVE VIEW!!
I have spent more time with afma then a lot of people put together. I'm getting really annoyed people think that this softness is the users fault. I have seen more examples like mine showing the same exact thing.
I have never been lucky with my lenses, check out which lenses I own, and I can assure you that NONE of them have EVER been at 0 setting and worked.
I'm not a n00b.
Sorry Viggo, but this answer wasn't for you, but for the OP.
I just had to post it after yours because you were faster
Okay, I'm sorry for taking it out on you then. I'm just pi$$ed that Canon screwed up and it's only me and a few other guys who seem to realize this isn't about the user, and however hard it is to believe, it is the camera and it has never been like that with another Canon, ever.... This reminds me of the 1d3 AF.....
The 5d3 is a spectacular camera, and I have been very excited about it long before buying it, and also very happy test shooting, but the softness really gets in the way of overly excitment and joy from using the camera.