I've been taking a night photography class through the Smithsonian, and we've had NO issues when out taking night shots with view cameras on tripods. I was shooting at the Lincoln, along the reflecting pool, and at the WW II, with nary a peep from a security guard. Same over at the Native American museum. Only time I've been hassled was one night I was trying to shoot the carousel on the mall, and the park police came zooming over to determine if I was doing it commercially. Which I wasn't.
I must say that of all the jurisdictions I've had to interact with around here, the Park Police are the most reasonable if you are respectful and explain to them what you're doing.