Anna, I can reproduce the problem. We'll need to check it out. Will your services be around for a while?
Nancy, are you able to print in other browsers? If so, can you share your web map publicly so I can look at it? When you say "print any of our layers" what type of layers are these? Are the running on ArcGIS Server? Are they publicly accessible from the internet (and not behind a firewall)? If they are behind a firewall, ArcGIS Online won't be able to print them.
Thanks,
Mike