The National Mall and Memorial Parks are a great places to hold a public event.  You get lots of traffic and a fantastic backdrop.  

While the challenges of outdoor events exist anywhere, the Mall and Memorials have many more.  

The spaces flip through multiple jurisdictions, National Park Service, The District of Columbia, and Architect of the capitol.  The preservation of the grounds is paramount and as a result rules are strict.  Proper permitting is also a must.