"docker run" fails with error on win10 1607

I am testing windows containers on the new 1607 Version (RTM) of win10 and have managed to install the WindowsServerCore and NanoServer images. But when I try to run a container it always fails with an error like this:

docker run nanoserver
C:\Program Files\Docker\Docker\Resources\bin\docker.exe: Error response from daemon: oci runtime error: exec: "c:\\windows\\system32\\cmd.exe": executable file not found in $PATH.

docker run -it windowsservercore cmd
C:\Program Files\Docker\Docker\Resources\bin\docker.exe: Error response from daemon: oci runtime error: exec: "cmd": executable file not found in $PATH.

I don't quite understand the error message. Is there a way to get further diagnostic information about this error and its possible causes?

Update: I have tried the updated tutorial on a different machine and it worked for NanoServer, but WindowsServerCore fails with:

The operating system of the container does not match the operating system of the host. (0xc0370101).

So, this feature seems to be quite unfinished!

I had posted this question on Stackoverflow first, but it got immediately downvoted, so I deleted it and posted the question here. Now I was quite surprised to find a very similar question with four upvotes on SO. But that aside, the answers of that post help troubleshooting windows-container problems.

And as I already mentioned in my question: containers on win10 are really "work-in-progress"!