I've noticed a few minor negative aspects of the 24-70E; there is more vignetting wide open but also some vignetting continues to my typical landscape aperture (f/9) and basically it must be corrected in software, otherwise it is too noticeable in snowy landscapes IMO. With the G version there was a bit of vignetting at 24mm, f/2.8 in the corners but stopped down the vignetting was below my threshold of perception. This is not a huge deal but I find it that often the profiles in Adobe software are not always accurate enough for perfect correction and I find this mildly annoying. (I took some shots accidentally in JPG mode as in the D750 the ISO and QUAL are close to each other) I would prefer lenses not to require correction after they're set at least 1-2 stops down from maximum aperture. With DXO's software I find the software correction to be more accurate though, but otherwise I'm not enthusiastic about their software as part of my workflow. I use it for photogrammetry since they have excellent distortion correction profiles (very accurate, and they automatically consider the effect of focus distance on the distortion which is crucial). Also the 24-70E's distortion is more complex in shape than what I found with the G lens. And finally as discussed above it seems I will have to purchase a longer panoramic rail to work with this lens.
However, the images from the 24-70/2.8E are very pleasing to my eye (assuming we correct the distortion and vignetting) and the AF works extremely well. I'm generally happy with the new lens. The images are clean, crisp, with vivid colours etc. and as mentioned many times already, the off center sharpness and CA characteristics are much improved from the G version.
I wish Adobe would put more attention to making more precise profiles that account for focus distance. Also it would be nice if they would take advantage of all the EXIF data instead of a minimum of it.