Among other things, the regs in question classify semi-automatic pistols - such as the ones that the DC police carry - as equivalent to machine guns, if a magazine of more than 12 rounds is AVAILABLE (even if the specific weapon to be registered does not get used with such magazines).
The new DC regs also require that the gun be unloaded and/or trigger-locked at all times EXCEPT when there is a "well-founded belief" that imminent use for self-defense will be necessary. This has been characterized as the "Wait, Mr Home Invader, please let me unlock my gun" clause.
The text of the actual complaint in the new case (PDF format) is at http://www.scotusblog.com/wp/wp-content/uploads/2008/07/new-heller-lawsuit-7-28-08.pdf
Edited 8/1/08 to reflect that it has been docketed.