It seems like the autoComplete plugin of jquery-ui doesn't work with with the Google Chrome and Firefox mobile browser. Everything works fine on their desktop versions. I'm sure it has something to do with how modals are displayed in mobile browsers but I can't figure out where the issue is.
The only thing I was able to rule out is that it's simply an issue with the z-index because if I trigger the autoComplete and then switch to another field that doesn't have autoComplete enabled it should still close the list even if it is in the background. But when I close the box I can see that the complete list is still visible. I assume that editor.autoComplete.js doesn't correctly hand over the input element to the jquery-ui autoComplete.
You can look at the live page in GC desktop with mobile view enabled in the dev tools as well:
http://live.datatables.net/hapitafa/4/
And a little side-question: Do Editor plugins have a npm package just like DataTables have? I'd love to let npm take care of potential updates and bundle everything using webpack.