I have PSN installed on a WordPress Multisite system. Is there a simple way to check all the sites and update the databases?

The patch button in the plugin backend only appears, if you overwrite the plugin files on the server without deactivating / activating the plugin (skipping the default plugin update process). In this case the plugin recognized a version mismatch and needs to run the patcher manually to update the necessary database tables.

If the plugin passed the default WP update process, the internal version checker gets updated and the patch button will not appear. So for updating from version 1.4 to 1.5 please copy / overwrite the plugin files and then deactivate and activate the plugin through your WordPress plugin backend. This is network compatible of course.

For future updates you can use the WP backend as PSN supports auto updating since version 1.5. You just have to insert your license code in the plugin options.