Washington was built on Potomac swampland, and the conditions that created that pestilential marsh continue to this day. Summers in Washington are nothing short of tropical, so if you are going there between May and September, you should pack as if you were taking a trip to Thailand. Wear light loose clothing and bring a handy water bottle. You will sweat a lot, and you should dress accordingly and be ready to drink lots of water.
Part and parcel of that swampy climate are Washington's infamous swarms of mosquitoes. The major type of mosquito in the D.C. area is the hardy Asian Tiger, which wields a nasty bite and seems to ignore most measures taken to repel it. Pack a bottle of deep-woods mosquito spray with a concentration of at least 50 percent DEET (the active ingredient of most mosquito sprays).
The museums of the Smithsonian and the office buildings of the federal government are huge. Walking across the front of one of these mammoths is not a one-block walk, but a two- or three-block walk. This makes distances around the Mall and in downtown D.C. deceptive. You can think, "Oh, that is only three blocks away," only to discover it is more like a mile. Those distances mean you will be doing a lot of walking to get from museum to monument, so you should bring a good pair of comfortable walking shoes. The alternatives are blisters and/or sore feet.