PCT Controller described an airspace deviation event when an aircraft was allowed to enter ZDC's airspace without required coordination/hand off; the reporter acknowledging a loss vigilance.

Narrative

While instructing on the ASPER departure scope; my developmental turned a CRJ2 toward the 'Charlie Gate'; where we feed the KRANT sector at 10;000 FT. IAD Tower then departed a northbound jet on runway heading off Runway 30; followed by a jet on a diverging heading inside the previous aircraft. At this time we were also working three other aircraft. The developmental turned the northbound aircraft. Since we had altitude; and since we were not talking with the second aircraft; restricted by the Tower to 3;000; I knew this would work; although this was not a preferred procedure. On initial contact with the second aircraft; he attempted a climb; which I quickly overrode. Basically; this created several situations we had to know correct and which I was hoping the developmental would address himself. I tried to help him see his errors; and explain why I overrode him. His concern with preceding turbo prop traffic was unnecessary; since it was nearly 20 miles ahead and climbing out of our airspace; and we had another conflict developing. Meanwhile; the CRJ2 had not received the necessary southeast heading through the Charlie Gate and had entered the adjacent sector; WOOLY. When this became apparent; I quickly turned the aircraft south and attempted to contact WOOLY. WOOLY was talking with KRANT; I guess they assumed KRANT was working the aircraft since it was on their tag after the ARTS hand off. I issued a late point out; and then talked with KRANT on how they wanted it. The coordinator also talked with KRANT. Although WOOLY had a jet climbing through the altitude of our aircraft; there was more than sufficient lateral separation; and I was able to ensure visual separation with their jet as well. I advised the Supervisor of the mistake and was relieved. He informed me that the recorded data showed no loss of separation with any other aircraft. I estimate the CRJ2 entered WOOLY airspace by ten miles. Recommendation; prompt turns through this gate as basic instruction on this position. I am well aware of the need to vigilantly monitor aircraft being vectored toward this gate; and simply allowed myself to be distracted from what I know I must do. I have no recommendations as I simply failed to monitor the position completely.