Global search breaks when not logged in / guest

There is two parts to this bug:

1) If you are not logged in you can use the global search and get to a page like:

http://moodle.local/search/index.php?q=the

But this always says 'No results'

2) There is a second part which is harder to reproduce and might be related to session timeouts, where if you then try to submit the same search form you will get a sesskey error. But you don't need a sesskey to use global search at all. But reloading the page which should set the right sesskey still doesn't work.