Plugin version 0.5.4.2
Network activated the plugin. Mapped domains on the Network Admin, Tools, Domains page. The domains are reachable as expected. However, if I change the settings for a mapping in the Network Admin, the changes aren't written to the database. Similarly, if I remove a domain mapping and try to add back the same mapping, it is not added.
Verified that the database is not being updated. Of course, manually inserting mappings into the database makes them appear in the Network Admin, Tools, Domains page.
On the other hand, going to an individual site's Tools, Domain Mapping page and modifying them there works correctly. Changes are saved.
This is not a showstopper for me since the site-specific or direct database insertion methods work, but wanted to report the issue for a future fix and share the workarounds in case anyone else runs into the same problem.