The issue with the menu is a conflict with the WP admin bar; if you're logged out or have the admin bar disabled in your user settings, it won't happen. The problem is that it's a random error and it can happen on one site and not another, even if both are using the same theme.
You can try adding the following code to the end of vertex/css_and_js.php to see if that fixes it for you:
<?php if(is_admin_bar_showing()&&is_home()){ ?>
<style>
#subMenusContainer{top:28px;}
.s5_sub_wrap_lower, .s5_sub_wrap_lower_rtl {margin-top: -28px;}</style><?php } ?>
The issue with the admin seems to be a server-specific problem. There have been a very small number of people who have had that issue with that version of the admin, but every time it has happened, the problem disappeared when they either switched hosts, or reinstalled the site from scratch.
If you can provide login and FTP information, I'll pass it on to Dave (he wrote the code for the admin) and we'll see what we can do.