An umbrella and a warm coat, hat, gloves etc - DC in January can be cold, wet, snowy, all of the above.
It would be good if you know someone in DC your son could call or call on in case of emergency, or just to connect. Growing up I knew the ex-wife of one of my dad's friends who went into witness protection (long story), she was a well connected DC political society maven who ended up being the highlight of my DC experiences, a real hoot. You don't need to know them well, if they're located in DC proper its a plus because your son will be able to reach them on foot or by subway/taxi.
For maps, the laminated folded walking map of DC is good as it actually covers everywhere he's likely to go, you can get them when you step off the plane in most bookstores and newsstands for $7.95, and they don't wilt in DC rain or snow. AAA will send you free road maps of Virginia, Maryland and Pennsylvania if you're a member.
I would tell my 16 year old to stick to his group, especially at night, and don't try anything too adventurous, like wandering the darkened streets southwest of the White House after midnight. Its been a few years but Georgetown is still good for teenagers, if they have time to hangout. Load his cell phone with the number for 2-3 DC cab companies (either lookup on DC travel sites ahead of time or note them at the taxi stand at the airport) - when in doubt of your surroundings in DC, call a taxi, get out safely. Stick to public places, for the inauguration there will be lots of them, he'll do fine.