ATR42 CREW ADVISED BY ATC THAT THEY DEPARTED WITHOUT TKOF CLRNC AT TLPC.

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WE WERE CLRED TO 'ENTER AND BACK TRACK RWY 9' BY GEORGE CHARLES TWR. THE CREW WAS PERFORMING TAXI CHKS DURING THE BACK TAXI WHEN TWR CALLED TO DELIVER THE ATC CLRNC. AFTER GIVING THE CLRNC; TWR SAID; 'ON THE TURN; CLRED FOR TKOF;' WHICH THE FO READ BACK. THE CREW HELD IN POS FOR 2-3 MINS WHILE COMPLETING DEP BRIEF; TAXI CHKS AND TKOF CHKS. THE FO'S MIKE SWITCH APPARENTLY STUCK DURING THE 'PREPARE FOR TKOF' PA; BECAUSE THE FLT ATTENDANT INFORMED THE CREW THAT THE TAXI CHKS HAD GONE OUT OVER THE PA. THE FO SWITCHED HIS XMIT TO VHF #1 AND UNWITTINGLY SENT TKOF CHKS OVER TWR FREQ. THE TWR CTLR APPARENTLY WAS PERTURBED BY THE DELAY AND THE OVER-FREQ CHKLIST. HE MAY HAVE ALSO THOUGHT THAT THE CREW WAS WAITING FOR TKOF CLRNC THEN JUST WENT WHEN THEY GOT IMPATIENT (PERHAPS READING THE CHKLIST OVER THE AIR TO REGISTER THEIR FRUSTRATION?). THESE ARE ONLY GUESSES AS TO WHY; BUT FOR WHATEVER REASON; THE TWR CTLR FORGOT THAT HE HAD CLRED THE ACFT FOR TKOF. AS THE ACFT PASSED 500 FT MSL; THE TWR CTLR SCOLDED THE CREW FOR TAKING OFF WITHOUT A CLRNC AND FOR READING THE CHKLIST OVER THE RADIO. THE CAPT CORRECTED THE CTLR; REMINDING HIM THAT HE HAD GIVEN 'ON THE TURN; CLRED FOR TKOF;' AND APOLOGIZED FOR THE COMS PROB. IN MY VIEW; THE CREW MADE NO ERROR. THE TWR MADE AN HONEST MISTAKE AND FORGOT THAT HE HAD ALREADY ISSUED TKOF CLRNC. NEVERTHELESS; THERE ARE 2 SAFETY ISSUES TO NOTE: 1) TWR MIGHT HAVE CLRED OTHER ACFT OR VEHICLES ONTO THE RWY WITH AN ACFT ABOUT TO ROLL. 2) DESPITE HIS BELIEVE THAT THE FLT WAS NOT CLRED; THE CTLR MADE NO EFFORT TO EITHER CLR OR STOP THE ACFT WHEN HE SAW IT START TO ROLL!