Coming from the 60D, which already performed admirably in low-light situations.
I shot a lot of low-light stuff (stage performances, etc) so high ISO performance is very important to me. Usable images at 20000 and 25600 ISO - those are shots that I probably couldn't get with any other camera. ISO102400 still has noticeable banding (hah) but I'll play around with it a bit and see if it's at all usable. Maybe for a super-grainy B&W conversion.
I found myself OVERexposing a lot because I'm used to having to push the 60D to its limits. Need a bit more practice to get my head around the wider ISO range.
Autofocus in low light is great, even for rapidly moving targets. I had a few misses but I'm sure I'll get better with experience and practice, and making sure I'm using the right AF modes. The only time it really struggled was with backlit/silhouetted targets - but I'm getting good enough at manual focusing that I was able to get some keepers.
I agree with Josh_30 about the location of the zoom button. Very difficult to get used to, and zooming (during image playback for focus review, and during live view for manual focusing) is a feature that I use A LOT.
Taking longer than I expected to get used to the additional joystick, after having the joystick integrated into the d-pad/wheel on the back of the 60D.
I LOVE the dedicated still/video switch. Having to whirl the wheel ALL THE WAY around to switch from video to M on the 60D was a hassle.
My midrange zoom was the Sigma 17-70 which is EF-S, so I got a gently used 24-70L to fit the 5D3. With the 24-70 (THE BRICK) attached, it is very heavy. But not so heavy that I won't walk around with it.
I LOVE the Rate button! LOVE IT. Way more than I should, really.