Yesterday I played a bit with the Findbar in LibreOffice, and changed it to look and behave more like in the applications like Firefox, or Evolution:
It is now hidden by default, and opens when you press Ctrl-f (for the old Search and Replace dialog I changed the keybinding to Ctrl-Alt-f), or when you choose Find in the menu. It opens at the bottom of the document, and you can close it again (and return back to the document) by pressing Escape. I also made the text entry wider so that more characters fits in there.
Enjoy! :-) - will be available in LibreOffice 3.4.