Integrate tests into the nightly build process

During a brief chat on IRC the following came up:
A next logical step after testing is integrated for issue queues would be to integrate tests into d.o.'s nightly build process.

The purpose for making this issue is simply to place the idea on the roadmap.

Things to consider when the time comes:
Tests need not stop a build (i.e. a failed test should not keep the build from happening or the package from being created), but it would be helpful if the results were published and/or included in the package.
It may be useful to include the tests themselves in the nightly build (or any release for that matter) so that people could conceivably run the same tests for themselves.