Any error in your JavaScript console?

Nope.
neither in the console nor in the log file.

There seem to be more (possible) JS issues:
Clicking on the switch to (de)activate a calendar has no effect.
The calendar is always visible.

Other parts work, the fullscreen button of the calendar is responding for example.

console.PNG (18,229 bytes)   

console.PNG (18,229 bytes)   

I tried this on three different browsers (Chrome, Firefox and IE). I disabled my ad/scriptblocker on Chrome. There is definitely no JS suppressed.

I do experience exactly the same issue on a multi domain setup of SOGo. In the 'network' view of the browsers' debugger I am able to see the search request going to the server and the results coming back (this works just fine and the results are correct and limited to the domain), but they never get displayed in any way.
When querying for 'demo' I can see a request going out to https://sogo.example.com/SOGo/so/user/usersSearch?search=demo that is receiving a response like this:
{"users":[{"isGroup":0,"c_email":"demo@example.com","cn":"Demo User","uid":"demo"}]}
Any idea how to debug the issue?

You can firs enable SOGoUIxDebugEnabled = YES;. Can you reproduce this on demo.sogo.nu ?

Thank you very much for getting back to me! The issue isn't reproducible on demo.sogo.nu.

It is also not reproducible on another single domain instance I operate. Just on a multi domain instance with several small domains this behavior is shown. When enabling SOGoUIxDebugEnabled the browsers' console shows an empty array after the XHR request. The server response to the XHR request looks identical on both SOGo instances and contains valid json.

Would it be possible to provide an access to your instance ?