If you plan a commercial photo shoot or video filming in the Washington DC area--including, in some cases, wedding photos--you might require a permit. In some instances, like the Vietnam Women's Memorial or the FDR Memorial, no commercial photography or filming is allowed at all. Your best bet, to cover yourself, is to get in contact with the relevant supervisory body. And I'd strongly recommend getting in touch with them well ahead of time to ensure enough time for your application to be processed if one is necessary. While some offices claim a very respectable turnaround of 4-6 days, it's entirely possible that others might take much longer.
And something to bear in mind is that in this economic climate, some local governments have begun to more strictly enforce the need for permits as a means of revenue raising.
Here is a growing list of relevant websites for applying for photography and filming permits for popular locations in the Washington DC area.
National Mall & Memorial Parks
Park areas administered by this office include more than one thousand acres and includes the original Mall area itself, many of the uptown circles, squares, and triangular parcels of land, East Potomac Park, and West Potomac Park.
George Washington Memorial Parkway
Park areas administered by this office include: Arlington House: The Robert E. Lee Memorial, Arlington Memorial Bridge & Memorial Avenue, Belle Haven Marina, Belle Haven Park, Clara Barton National Historic Site, Collingwood Park, Columbia Island Marina, Claude Moore Colonial Farm, Daingerfield Island, Dyke Marsh Wildlife Preserve, Fort Hunt Park, Fort Marcy, Glen Echo Park, Gravelly Point, Great Falls Park, Jones Point Park, Lady Bird Johnson Park, Lyndon Baines Johnson Memorial Grove-on-the-Potomac, Mount Vernon Trail, Netherlands Carillon, Potomac Heritage Trail, Riverside Park, Roaches Run Waterfowl Sanctuary, Theodore Roosevelt Island, Turkey Run Park, U.S. Marine Corps War Memorial ( Iwo Jima Memorial), Washington Sailing Marina, and Women in Military Service For America Memorial.
Arlington National Cemetery
The Cemetery provides this guidance:
Photography is permitted within the grounds of Arlington National Cemetery. Public use of a tripod or lights is not permitted without permission from the Office of Public Affairs. News photographers and videographers need to make arrangements with the Office of Public Affairs ((877) 907-8585).
We ask media and cemetery visitors/tourists seeking to photograph those visiting gravesites to respect the solemnity of Arlington National Cemetery by refraining from taking pictures or filming someone who is visibly mourning and asking for permission to film or photograph those visiting a gravesite. Many are very open to talking with media and cemetery visitors about their loved ones and want to see their loved ones honored and remembered.