Same problem here (with firefox AND safari and chrome),
editor links set to relative,
containing page : ="/Admin/Pages.aspx?pageID=121"
If i set a link to an anchor tag,
in firefox & co, the editor takes the containing page in the url: <a href="http://cutesoft.net/Admin/Pages.aspx?pageID=121#a1"></a>
while working ok in internet explorer : <a href="#a1">
simply opening the page with IE recovers all links in the editor to the correct relative hre,
while opening in other browsers trash the links...
internet explorer 8