On the advanced search page we offer "fewer" and "more options" for the patron. Which is offered by default, can be set using the expandedSearchOption system preference. It is annoying for a user who prefers the 'more options' if his/her selection doesn't stick over multiple searches. They have to switch to the 'more options' every time, as the choice isn't remembered. It would be nice if Koha remembered which form the user used last.
I'd tempt to remove the pref and use sessionStorage, but it won't work at the OPAC if JS is disabled.
Thinking of our libraries there seems to be a difference in what people like to be the default - so I am not sure about removing the pref.
I am not sure when that was fixed, but there is definitely a Cookie for it: https://wiki.koha-community.org/wiki/Use_of_Cookies (search_path_code)