Focus and search box issues

[vinc17fr]

After doing a search on https://codesearch.debian.net/ the results cannot always be scrolled with the keyboard (page up, page down, up and down arrow keys). It seems that this is due to the fact that the search box (top / right) grabs the focus and keeps it, even when I click somewhere else in the window. This is not always reproducible.

I had this problem with Iceweasel 43.0.2, and on another machine with Firefox 43.0.3, when I type Page Down, a drop down menu corresponding to the search box appears... at a wrong place: