Having worked in northern Virginia about 30 years ago, I can GAHROHNTEE the idiots driving cars with diplomatic plates get by with a lot of serious stuff that would see you or I in jail for the night.
US citizens have been crippled and killed by drivers with diplomatic plates who then get off Scott free. At most the offending driver is recalled to their native county.
Nowadays the issuing of Diplomatic plates is done by the Dept of State, Office of Foreign Missions and there have evolved several different types of plates as shown at the link.
http://dcplates.com/OFM.htm
I concur with what you said here. At the same time the same DC police (who of all departments in the USA should know better) still conducts idiotic stops on diplomats.