You should be able to select text in those windows, but not edit or delete it.
You can actually change the message in the pop up window, which is quite odd.
OS X: version 10.11.4 (build: 15E65)
Docker.app: version v1.11.1-beta10
But still applies to
Docker.app: version v1.11.1-beta11
Steps to reproduce the behavior
Open up those windows via the Menu Bar icon of Docker > Dashboard… or Logs…