I was having problems using Internet Explorer 7 and it doesn't work with IE 6 either. I use Safari on my Mac and use Firefox elsewhere, but on the university computers I have no other option. What I have done is set-up forwarding in MobileMe to send all email to my GMail account as well, with GMail set to look like it is sent from MobileMe. Anytime I need to go on Me.com because I don't have my iPhone or Mac handy then I just hop on GMail, which is a lot quicker and more compatible than the Me.com interface which only seems to work great on Safari. Even GMail is quicker than Me.com in Safari. C'mon Apple Me.com doesn't have to be that pretty just give us a slick, fast, interface that works on all browsers that is as quick as GMail, Yahoo Mail and Hotmail.
The problem could be caused by the adblocking feature as described by Daveecee in another post: