Unfortunately the RWD theme contact form contains an invalid link on the post target of the form.
Currently the link is:
<form action="<?php echo $this->getFormAction(); ?>" id="contactForm" method="post">
However, for the form to work correctly, you should change it to:
<form action="<?php echo Mage::getUrl(); ?>contacts/index/post/" id="contactForm" method="post">
Hopefully that should fix it for you!