ZJX CTLR PROVIDING OJT EXPERIENCED OPERROR AT FL245; TRAINEE FAILED TO NOTE CONFLICTING ALT ASSIGNMENT AND INCORRECT ALT READ BACK NOT REALIZED.

Narrative

I WAS TRAINING A PERSON ON THEIR FIRST RADAR POS AND THEY ISSUED A CLB TO ACFT X TO FL260. ACFT Y WAS LEVEL AT FL240 WBOUND WAITING FOR HIGHER; CLR OF TFC. I WAITED FOR HALF A MIN FOR THE TRAINEE TO CATCH HIS ERROR; BUT HE DIDN'T; SO I ISSUED AMENDED ALT TO ACFT X TO FL230. AS I UNKEYED THE MIKE; SOMEONE READ BACK 'UNINTELLIGIBLE FL230' ACFT Y WAS ISSUED A CLB CLRNC TO FL260 LATER. AS THE ACFT GOT CLOSER; CONFLICT ALERT ACTIVATED AND WE SAW ACFT X GOING THROUGH FL230. ACFT Y STILL HADN'T CLBED ALMOST 30 SECONDS AFTER CLB WAS ISSUED. ACFT Y GIVEN IMMEDIATE CLB AND 30 DEG R TURN FOR TFC. RELEVANT ITEMS: SECTOR WAS VERY BUSY DUE TO MIL ACFT JOINING UP TO REFUEL ON AR600. ALL ORLANDO ACFT NEEDED DSCNT TO FL300 FOR MIL ACTIVITY FURTHER S (ORCA) INSTEAD OF LEAVING THEM AT ALT. TRAINING IN PROGRESS. SEPARATION WAS LOST BECAUSE EVERYONE AT THE SECTOR MISSED THE READBACK (4 PEOPLE) AND ACFT X NEVER AMENDED THE ALT. PLT CHKING ON CLIPPED HIS CALL SIGN AND THAT IS WHO WE ALL THOUGHT WAS ACFT X READING BACK ALT OF FL230. REQUIRING ALL PLTS TO LISTEN BEFORE CHKING ON A FREQ WOULD HELP PROBS OF STEPPING ON THE CTLR CLRNCS AND PLT READBACKS. IT HAPPENS QUITE OFTEN IN THIS AREA. EVERYONE JUST KEYS UP THEIR MIKE WITHOUT LISTENING FIRST. MAKING THE MIL DO THEIR PRACTICING OVER THE OCEAN. THEY HAVE ALL THIS OCEANIC AIRSPACE (WARNING AREAS) THAT THEY TAKE FROM THE CTRS; YET THEY STILL HAVE REFUELING AND SPECIAL ACTIVITIES IN THE MIDDLE OF ALL THE SECTORS WORKING PAX AND GA ACFT. THIS AIRSPACE IS BECOMING MUCH TOO BUSY TO BE WORKING THESE ACTIVITIES THERE. OR; DO IT AT 3 IN THE MORNING WHEN IT'S NOT SO BUSY.