A B737-700 CAPT DEPARTING MDPP COMMENTS ON THE POOR COM QUALITIES AND A DEP CLRNC MIX-UP RESULTING IN AN AIRBORNE TFC CONFLICT.

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THE CTL TWR XMISSIONS WERE HORRIBLE THAT DAY. XMISSIONS; BOTH INBOUND AND OUTBOUND; WERE EITHER FAINT; GARBLED; INDISTINCT; OVER-MODULATED; OR HAD BACKGND NOISE. ALL INSTRUCTIONS WERE ISSUED WITH A STRONG SPANISH ACCENT. WE ASKED FOR REPEATED CLARIFICATION WITH EVERY XMISSION. OUR OUTBOUND ATC CLRNC HAD TO BE REPEATED 3 TIMES. WE WERE IN POS FOR TKOF ON RWY 8. OUR CLRNC WAS TO TURN ON COURSE AND CLB TO FL180. WITH THE TKOF CLRNC CAME A CHANGE TO MAINTAIN 5000 FT. WE READ BACK THE CHANGE AND DEPARTED. IN RETROSPECT; I CAN SEE THAT THE MDPP TWR ALSO MEANT TO CHANGE OUR CLRNC TO MAINTAIN RWY HDG; BUT THEY DID NOT. NEITHER ME NOR MY FO HEARD THE TWR SAY 'MAINTAIN RWY HDG.' WHEN MY FO RESPONDED TO THE TKOF CLRNC; HE XMITTED OUR ALT CHANGE ONLY. ON DEP; WE BEGAN OUR TURN ON COURSE; WHICH WAS THE POP 354 DEG RADIAL. WE WERE TURNING TO A HDG OF 330 DEGS TO INTERCEPT WHEN WE SAW A B767; AIRLINE UNKNOWN; XING FROM R TO L. HE HAD JUST RPTED TO THE TWR THAT HE WAS AT 3000 FT. WE SAID THAT WE HAD THE TFC IN SIGHT AND WOULD STOP OUR CLB AT 2000 FT. THE B767 PLT SAID THAT THEY WOULD MAINTAIN 3000 FT. WE PASSED 1000 FT BELOW OUR TFC AND ABOUT 1 MI BEHIND HIM. WE THEN CONTINUED OUR CLB TO 5000 FT. MY FO THAT DAY DID A GREAT JOB ON THE RADIO; UNDER DIFFICULT CONDITIONS; AND HELPED TO CLARIFY OUR INTENTIONS TO THE TWR AND THE PLTS OF THE B767. TO COMPENSATE FOR THE POOR QUALITY OF THEIR RADIO EQUIP; AS WELL AS THEIR HARD-TO-UNDERSTAND ENGLISH; THE MDPP TWR PERSONNEL SHOULD NOT CHANGE THEIR ATC INSTRUCTIONS AT THE LAST SECOND. ADDITIONALLY; IF A CLRNC IS NOT READ BACK TO THEIR SATISFACTION; THEY SHOULD QUESTION IT.