Not sure why we've wandered onto dynamic range, as I was using a 5dMkIII a bit I can comment though, very nice camera but DR wise yes it clearly lags rivals, and it's not as good as some crop sensor cameras in that dept, DR has only marginally increased with Canon over the years.
However the main problems that face mirrorless remain, price relative to other normal crop sensor and FF bodies, and the system.
People can point to the new wave of modern designs, but these come with a higher challenge for optics (with the lens sitting closer to the sensor) this was and remains a problem for designers with distortion and fall off much more of a problem than normal DSLR type designs.
ILC's are interesting, but they are not going to represent the future for many buyers simply because they don't offer a compelling reason to move to them. And looking at some of the prices makers are charging, the camera industry is frankly fooling itself. In the last decade there has been a huge reduction in the price of consumer electronics, from computing to televisions, audio equipment and other items. Yet the camera industry feels it can remain immune to this, and they are horribly wrong... this is one of the reasons for the decline in sales of cameras with makers desperately trying to get premium prices (on higher end compacts and cameras) when the market simply isn't going to take it. We've loads of cameras, and most people won't be updating very often, and until the industry works out that they're overpriced, they won't get the sales on other items to make the profits.