Customize display order of posts by a simple drag-and-drop Ajax interface, now with support for custom post types and custom taxonomies.
Try opening up your WP admin and browse to your postMash page, then take a look at the page source. Check if the prototype or scriptaculous scripts are included in the header. If so then the next step is to track down the offending plugin, which you can do by disabling each of your plugins in turn and checking when the scripts are no longer included.
Yes, by default posts are shown in reverse chronological order, to show the posts in the order you set in postMash you will need to use different code to display your posts. Look in the install section for an example.
Any good up-to-date browser should work fine. Tested in Firefox, IE7, Safari and Opera.