WebParts Cross- browser drag and drop is a very common issues on ASPNET WebPart Framework.. Basically WebParts doesn't support the Drag and Drop feature in Firefox browsers and this known to be a BUG for ASPNET Webpart Framework.. To get things working in all browsers including the cross browser drag-and-drop feature then you would need to use Visual studio 2008 / VWD 2008 with latest version of the Microsoft ASPNET Futures (AJAX Control Toolkit 3.5)..

For more detail information then i would suggest you to read the following article below

http://waitink.blogspot.com/2008/06/ajax-web-parts-part-1-drag-and-drop.html

We also discuss the issues in the following links below

http://forums.asp.net/t/1277540.aspx

http://forums.asp.net/p/1087200/1943716.aspx#1943716

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