LibreOffice 3.4.4 is not autodetecting the JRE supplied by OpenJDK6. Further, it does not allow you to navigate to the installed JRE.
How-To-Repeat: Install libreoffice-3.4.4 and openjdk6-b24 using their packages. In LibreOffice, go to Tools -> Options -> Java. The box is checked for "Use a java runtime environment" but the JRE is not autodetected. Clicking the Add button will navigate directories, but will not allow you to pick the JRE (i.e. a file within a directory). If you instead select the parent directory containing JRE, the page refreshes and expects you to select again.
Over to maintainer (via the GNATS Auto Assign Tool)
Fixed with 3.5.2, thanks for reporting