The biggest concern has to be the hole the Capitals have at second line center. None of the options within the organization - Brooks Laich, Marcus Johansson, Eric Belanger, and Tomas Fleischmann - are particularly appealing, and the team needs someone who, working with Alexander Semin, can give the Capitals a second elite scoring line.
A lesser, but still valid concern, is the team's defense. Five of the team's six nightly defensive spots should be spoken for, and although the Caps will probably hold on to John Erskine and Tyler Sloan for depth purposes, neither is a good option for a sweater on a regular basis. An NHL defenseman of any ilk, from top-pairing quality to third-pairing depth guy, would help and the team has enough flexibility to fashion a capable defense with just about any addition. Who the team ultimately winds up with, be it via trade or free agency, will depend as much on the player's cap hit and the length of his contract as anything else.
For a full primer on the Caps as they prep for July 1, check Japers' Rink.