Dynatable is released under the Free Software Foundation's GNU Affero General Public License (AGPL).
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Currently the testing process consists of opening the Dynatable documentation (source code here) in each browser and making sure every example works. This is fine for the initial release, since it serves the dual purpose of helping us write the documentation and having a written functional use-case at once. However, one of the top priorities now is to automate each use-case in the docs as a test case within an automated test suite.
If anyone out there thinks this sounds like fun, please contact me or even go ahead and create an issue/pull request. Otherwise, it will be at teh top of my priority list until I can get to it.