ZDC CTLR PROVIDING OJT DURING BUSY TFC; FAILED TO NOTE A DESCENT CLRNC ISSUED BY THE STUDENT CTLR; OPERROR EXPERIENCED AT APPROX FL370.

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I TOOK CTL OF SECTOR 38; TAR RIVER SECTOR; WITH A DEVELOPMENTAL. THE SECTOR HAD A LOT OF COMPLEXITY AND VOLUME; 19 ACFT ON FREQ. THE DEVELOPMENTAL IS FAR ALONG IN TRAINING; THIS IS HER LAST SECTOR. THERE WAS ANOTHER DEVELOPMENTAL ON THE D-SIDE (ASSISTANT) POS WHO WE WRONGLY ASSUMED WAS CERTIFIED. WE SOON LEARNED THAT HE/SHE WASN'T. THERE WERE MULTIPLE PRIORITIES THAT NEEDED TO BE ACCOMPLISHED. 1) A NON-RVSM ACFT NEEDED TO BE TRANSITIONED DOWN TO NON-RVSM AIRSPACE. 2) AN IMMEDIATE POINTOUT WAS NEEDED TO AN ADJACENT SECTOR; D-SIDE DEVELOPMENTAL COULD NOT HELP US. 3) A SHORT NOTICE; TMU DIRECTED BOS REROUTE WAS BEING REQUESTED. THE SUPVR ON DUTY ASKED ME ABOUT THE ACFT; WHICH WAS A DISTR FROM WHAT THE DEVELOPMENTAL WAS DOING. AT THIS TIME HE/SHE ISSUED THE CRITICAL DSCNT TO THE A319 AND I DIDN'T HEAR IT. 4) THERE WERE 3 WASHINGTON DC METRO ARRS THAT NEEDED TO BE TRANSITIONED FROM FL370 TO FL270 IN THE SPACE OF 60 NM THROUGH A HIGH VOLUME OF OPPOSITE DIRECTION; SBOUND TFC. I FELT THAT THE DEVELOPMENTAL WAS IN FULL CTL AND ACCOMPLISHING ALL THE NECESSARY TASKS. HE/SHE PUT A JRING (5 NM) ON THE HS25 SBOUND WELL IN ADVANCE IN ANTICIPATION THAT HE WOULD BE TFC FOR THE DSNDING METRO TFC. WHEN HE/SHE ISSUED THE DSCNT TO THE A319 (IAD) I MISSED IT AS NOTED ABOVE #3. WHEN I SAW IT; I PROJECTED HIS FLT PATH WOULD PASS BEHIND THE JRING OF THE HS25. THE A319 WAS TURNED TO THE R; 4.5 NM/500 FT. OTHER FACTORS: ZDC IS ISSUING MANDATORY OVERTIME TO NON VOLUNTEERS ALMOST WEEKLY. THERE IS AN ENORMOUS AMOUNT OF OJT OCCURRING IN ORDER TO CATCH UP WITH STAFFING. ADD THE TSTMS/DEVS -- I AM EXHAUSTED!