Several readers have raised the question regarding the extraterritorial rights granted to an Embassy and its personnel. For those interested, Wikipedia has a good write up on Embassy personnel and grounds. I extracted portions of that write up to create the following. There are also many official documents that provide information on extraterritorial rights.
Contrary to popular belief, diplomatic missions do not enjoy full extraterritorial status and are not the sovereign territory of the represented state. The premises of diplomatic missions remain under the jurisdiction of the host state while being afforded special privileges (such as immunity from most local laws) by the Vienna Convention on Diplomatic Relations. The rights that a host country grants a foreign power in establishing an Embassy in the host country are determined by diplomatic negotiations.
One of the specific questions asked by my readers is 'Does Doug need a building permit?' As a general statement, the host country provides the buildings, facilities, grounds, etc. to the foreign Diplomatic Mission. Under these conditions, there is no construction so a building permit would not be required.
I am not positive that a foreign government would require a building permit if it were to purchase a piece of property and construct buildings on the property that will be used as the Embassy. However, I strongly suspect that a building permit would be required.
As far as my story goes, I am of the opinion that a building permit is required. It is also a valid point that a building department's function is to ensure that a new structure is constructed in a manner that will ensure that it is safe for occupancy and that any applicable health codes are met.