Although I set the setting "Site Icons" to On DuckDuckGo doesn't display the favicon in the search results if I'm using the basic theme. With other themes this issue doesn't happen.
Interestingly it also resets the setting to "Off" if I'm looking at the settings later.
But much more confusing is that if you enable the WOT icons and the favicons then it's working correcty and displays them both.
So with basic theme enabled you should hopefully be able to reproduce it this way:
Enable site icons, disable WOT icons --> Save settings --> Search for something --> Favicons aren't displayed
[All steps before] --> Go to settings "Appearance" again --> The settings for Favicons is off
It happens similar with the option "Result URLs above snippet". If I disable it while using the basic theme it will be reset to the default which is "On" with the basic theme.
BTW another issue is that the "Save settings" button is behaving differently - sometimes it redirects you back to your last site - sometimes it doesn't and just bumps you to the top of the settings page.