Currently the dragable field “User name and password” mashes together:
I don't see this as very user friendly, especially the placement of the Current password.
Username, E-mail address and Change Password should be separate dragable fields in Manage Fields.
Current password should be made smarter and only show when it is needed to be entered, i.e when a user is changing the e-mail or password. Either Drupal will notice that changes are made and make it visible, or it will be asked for when the user clicks on the Save button.
Preferable these changes should also be backported to Drupal 7.