I had the same hope for Docker, that it would ease reproducible builds. It quickly became clear to me how much work still needs to be done for that to be realistic. I maintain a packaging of Meteor using Docker designed to increase reproducibility (https://registry.hub.docker.com/u/danieldent/meteor/). It does some checksums on the Meteor code, but the build process itself introduces entropy, and Dockerfile doesn't really have the primitives to make it easy to prevent that.

Many many build processes have hidden from-the-network dependencies which are yet another huge source of problems (both in terms of having high-availability for the build process and in terms of understanding exactly what is getting built).

All of the upstream Docker images (including the bottom base images which most people never look at carefully) would need to be built in a reproducible way. And the Docker code would need to actually verify checksums more carefully than it currently does.

Having projects like Debian doing work like this will make it a lot easier for everything else to become reproducible. Which in addition to the security benefits is also pretty useful when bug hunting - having a system that makes it clear which (if any) of your dependencies changed narrows the list of things which need to be checked when something breaks. Ubuntu Core, Snappy, and Nix are also on my list of things to watch in this area.