Symptoms

When I click the "Application" button, it appears as if nothing happens and eventually an empty SharePoint page is displayed.
 

Diagnoses

After some investigations, we found that the "default groups" that we assign rights to, (site owners, visitors, contributors etc.) was deleted.
 

Resolution

Re-creating the groups and adding users to said groups did not do the trick. We had to assign rights on the App catalog site as well. After that, we were able to run the registration wizard and the application button worked as expected.