B727-200 CREW HAD TAILSKID CONTACT ON RWY AT TKOF ROTATION AT MIA.

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DURING THIS TKOF; USING 'REDUCED THRUST;' AND SOMETIME SHORTLY AFTER ROTATION WAS INITIATED; I FELT A VERY SLIGHT VIBRATION; LASTING ONLY AN INSTANT. THE ROTATION WAS COMMENCED AT VR; AND WAS ACCOMPLISHED SMOOTHLY AND SLOWLY; AT A RATE OF APPROX 2 DEGS PER SECOND. I WAS REFING THE PITCH DURING ROTATION WITH THE ATTITUDE INDICATOR; AND MY INTENT WAS TO ALLOW THE ACFT TO FLY OFF WHEN IT WAS READY. I RECALL THAT THE PITCH INDICATED LESS THAN 10 DEGS WHEN THE VIBRATION OCCURRED. THE LNDG GEAR WAS RAISED AT THE 'POSITIVE RATE' CALL. AFTER WE WERE AIRBORNE; I ASKED THE CREW IF THEY NOTICED A 'VIBRATION.' MY FO AND THE FE DID NOT FEEL OR NOTICE WHAT I WAS REFERRING TO. THERE WAS A FLT MECH IN THE OBSERVER'S SEAT; WHO STATED TO ME THAT HE DID FEEL SOMETHING; AND THOUGHT IT MIGHT BE A BAG SHIFTING IN THE CARGO COMPARTMENT. THE FE THEN RPTED THAT THE TAILSKID LIGHT WAS ON. AFTER SWITCHING TO DEP CTL; IT WAS RPTED TO US THAT THERE WAS SOME DEBRIS ON THE RWY; RPTED BY A PERSON ON THE GND; AND THEY WOULD GET BACK TO US. WE CONTINUED TO CLB AND THE ACFT WAS PRESSURIZING NORMALLY. WE ALL ASSUMED IF SOMETHING HAD FALLEN OFF THE TAILSKID; PREVENTING IT FROM RETRACTING; THAT WOULD LIGHT THE 'TAILSKID' LIGHT; BUT ALL OTHER SYS WERE NORMAL. AS THE FLT TO TALLAHASSEE WAS ONLY 1 HR; AND WE HAD ADEQUATE FUEL (IN CASE THE TAILSKID WAS DOWN); WE CONTINUED NORMALLY; WHILE CAREFULLY TRACKING THE FUEL BURN; AND LANDED WITH NO OTHER PROBS. AN AFTER LNDG INSPECTION REVEALED A PART OF THE TAILSKID FOOT WAS MISSING; ALONG WITH THE COMPRESSION CARTRIDGE; AND THE ACTUATOR/DOOR WAS DAMAGED. I DON'T BELIEVE THAT THIS PART WAS INTENDED TO TAIL OR SEPARATE AS IT DID; JUST COMPRESS WHEN IT WAS HIT. THE INDICATOR CLIP WAS NOT SHEARED; NOT WAS THE CHAIN BROKEN; WHICH WOULD BE A SIGN OF A TAIL STRIKE. ADDITIONALLY; ON THE FERRY FLT BACK TO MIAMI; WE WERE UNABLE TO PRESSURIZE; AND WE FOUND A HVY; CLOTH-LIKE MATERIAL OF SOME SORT STUCK IN THE L OUTFLOW VALVE; WHICH PREVENTED THE VALVE FROM FUNCTIONING PROPERLY. ON APR/XA/01; MY DIRECTOR OF OPS REVIEWED WITH ME THE FLT DATA RECORDER READOUTS; WHICH CONFIRM THE CREW RECOLLECTION THAT THE ACFT WAS NOT EXCESSIVELY ROTATED. IN FACT; THE ROTATION FROM INITIATION TO 10.3 DEGS TOOK ALMOST 8 SECONDS. AT THE 'ASSUMED LIFTOFF POINT' (DETERMINED BY THE FIRM THAT READ THE FLT DATA RECORDER); THE PITCH WAS LESS THAN 10 DEGS; AND THE AIRSPD WAS 141 KTS (VR WAS 132 KTS); EXACTLY AS IT SHOULD BE. NO ONE CAN UNDERSTAND WHY; USING THE PROPER ROTATION TECHNIQUE AS DESCRIBED IN EVERY AVAILABLE BOEING MANUAL; COMBINED WITH NUMEROUS YRS OF CUMULATIVE EXPERIENCE WITH THE B727; THAT THIS TIME THE ACFT DID NOT FLY OFF AS EXPECTED; WITHOUT DRAGGING THE TAILSKID.