Hi,
Just in case anyone ran into this issue:
You get this red warning that you need to update your Drupal core to 6.15, you go ahead with the download, upzip all files into the htdocs folder locally (or public_html on the server), and all the site's theme is messed up!
Quick solution: remember to copy back your sites + themes folders from the previous setup. If you overwritten them, try to get them from a recent backup.
As a good practice, I usually copy contents of a folder to a temporary location before overwriting them - just in case!