1) The DOF is incredibly thin. Love it!
Yep. 1.3-stops thinner, to be exact (i.e. if you set the aperture to f/2.2 on your 5DII, you'd get the same DoF if you framed a similar shot on your 60D af f/1.4).
2) Quite a few of the images are soft. I am manually focusing the majority of the time, and even tried AF. It still seems soft. The IQ seems comparable to my 60D which is not what I was expecting. The lens has always worked flawlessly for me, but something just seems off.
Three things going on here. One is that the lens does have some halation at f/1.4-f/2 (a glow-like effect). Two is that your autofocus might be off. For the AF shots, you may need to perform an AF microadjustment (ideally with a tool like the LensAlign MkII or SpyderLensCal) - AFMA allows you to fine-tune the AF performance of a lens to a body, and is a very nice feature that the 60D lacks. That's especially important for wide aperture lenses where the thin DoF reveals any small errors in focus.
But, you manually focus most of the time, so AF isn't the issue? If you are using Live View at 10x to manually focus, then it's likely just slight lens softness at wide apertures. But if you're focusing using the viewfinder, your focusing screen is the problem. Stock focusing screens in all current cameras are laser microetched to be brighter with slow lenses (so they work better with consumer f/3.5-5.6 zooms). A consequence of that microetching is that the DoF yo see in the viewfinder is equivalent to about f/2.5, even with a wider lens. Try an experiment - normally when looking through the VF, the lens aperture is wide open, but when you use the DoF preview button between f/2.8 and a narrower aperture, in addition to seeing the true DoF you also notice the VF getting darker. But with your 50/1.4, try holding the DoF preview button and adjusting the aperture from f/1.4 to f/2.5 - notice, the VF isn't getting any darker. Nor is the DoF changing, because the VF won't show it. So, you are manually focusing at f/1.4, but judging focus based on the deeper DoF of f/2.5 - meaning you might miss when you get the real DoF in your image.
The solution is the Canon Eg-S focusing screen, which is a matte screen that will show the true DoF of your fast lenses. Great for MF with fast primes, but with an f/5.6 lens indoors, the VF will be really dim.
3) When I shoot in full auto, the ISO only reaches to 3200. When shooting manually, I am able to kick it up to 6400 (yes the noise is horrific) but why might this be?
The 60D has user-selectable max ISO for Auto ISO, previous cameras do not. So, Auto runs from 100-3200 and there's nothing you can do to change the max (or the min directly, althoguh using HTP will up that to 200).