Although the Replace dialog (ctrl-h) is selected and the Search For field accepts an ordinary letter as input, attempting to type a nonbreaking space or a nonbreaking hyphen into that field results in it being typed instead into the underlying document at its invisible insertion point (the dialog being open renders the document's insertion point invisible even if not blocked from view).

Bug 89573 is closely related. Bug 68151 seems related but turned out to be unrelated.

I uninstalled and reinstalled Writer on Aug. 16, 2015, and got a different user interface look, but still received only version 4.3.7.2, even though that was not offered via LibreOffice.org a few minutes later, so apparently that version is still being supported. If the problem still applies to a later version, addressing that will be enough.

My hardware is AMD.