I am not able to drag and drop my widgets in order to change their order from wordpress admin area. Many of the wordpress users have reported the same issue. Hence, I have searched the solutions and performed in my blog which has resolved the problem. Hence, I have provided the solution here which may help to resolve others problem too.
1. Generally, it is due to the plugins which creates this kind of problem….so you can either deactivate all plugins from database…for the details refer this:
And reactivate one-by-one to find culprit…or rename the Plugins directory via FTP.
2. From wordpress admin area -> Appearance-> Widgets under Screen options, try the Enable Accessibility Mode.
3. Delete or refresh the browser cache.