DA20 FLC OVERSHOT ASSIGNED ALT AND CONFLICT WITH A310. PLT QUESTIONS INCORRECT READBACK NOT CHALLENGED BY ZID.

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THIS APPEARS TO BE A HEARING; READBACK; HEARING PROB. INITIAL DSCNT FROM FL390 TO FL330. I READ BACK CLRNC; RESET ALT ALERT AND PRESSURIZATION. BEFORE LEVEL AT FL330; RECEIVED CLRNC TO FL310; READ BACK BY ME; RESET ALT ALERT AND PRESSURIZATION. NEXT CLRNC I HEARD; WAS TO FL240; READ BACK FL240. RESET ALERT AND PRESSURIZATION TO LNDG FIELD ELEVATION. NOT CHALLENGED ON READBACK BY MY PARTNER; WE BOTH AGREED ON FL240; OR BY CTLR. HAVE BEEN TOLD BY ZID TAPES HAVE OUR CLRNC TO FL280; AND THEN MY READBACK TO FL240. BOTH CLRLY HEARD ON TAPE. MY QUESTIONS: 1) WHERE DID MY PARTNER AND I GET 240? 2) WHEN I READ IT BACK TO CTLR; WHY WAS I NOT CHALLENGED ON MY ERROR? DID NOT SEEM TO BE A BUSY SECTOR; NOT A LOT OF TFC ON FREQ. LEAVING FL277; CTLR ASKED FOR OUR ASSIGNED ALT. REPLIED FL240; HE SAID 'NO; CLB TO FL280 AND A 60 DEG L TURN.' OTHER ACFT GIVEN A R 40 DEG R TURN. WE SAW OTHER ACFT VISUALLY AND ON TCASII. NO TCASII ALERTS OR WARNINGS. I DO NOT KNOW WHERE I GOT FL240 FROM; BUT MY PARTNER AND I HAD AGREED ON THAT ALT; AND THAT WAS WHAT I READ BACK TO CTLR.