Python 2.x has a test called test_xpickle which confirms that pickles can be successfully passed back and forth between different versions of Python.  This should be forward-ported to 3.x, and include tests between the python under test, 3.6, 3.5, 3.4, and 2.7, for each protocol available to each version.  If feeling adventurous, you could even go as far back as 3.0 :)

Ideally, this should also run on Windows by making use of the `py` launcher, and possibly even include 32- and 64-bit versions of each Python on Windows.