To search, you currently select a tree entry in ldap browser, then new -> search
I find this not very intuitive to have to click new to get a search dialogue (I know, this is the Mac "everything is a document" spirit , for me, the collection of search results is useless, especially, as it is hard to re-use them (scroll down, find the last, change properties, double click).
I suggest to add an additional context menu "Search" to the tree entries, which would immediately get a search dialog. If you allready had done this previously, you get the previous search settings.
This menu entry should be right at the top. Also, there should be an entry "show last search result".
show last search result
I think, this is what you mostly need, I never need or use the list of old searches.