ACR FLC DECLARES EMER WITH SPLIT FLAP PROB'S ; BUT EXECUTES A GAR DUE TO CTLR TECHNIQUE AND VECTORING.

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DURING CONFIGURATION OF ACFT FOR APCH; IT WAS DISCOVERED WE HAD A SPLIT (ASYMETRICAL) FLAP CONDITION. L FLAP INDICATING UP AND THE R FLAP INDICATOR AT 1 DEG. WITH ASSISTANCE FROM PIT APCH CTL FOR EXTRA TIME AND VECTORS TO COMPLETE THE ABNORMAL CHKLIST; WE WERE THEN VECTORED FOR A VISUAL APCH TO THE LONGEST RWY. FA'S WERE BRIEFED UPON COMPLETION OF THE ABNORMAL CHKLIST AND WERE ADVISED OF THE HIGHER THAN NORMAL APCH SPEED (VREF + 40). COMPLYING WITH COMPANY POLICY FOR A FLT CTL PROB; WE DECLARED AN EMER WITH APCH CTL ADVISING THEM OF FUEL AND PAXS ON BOARD. APCH AND LNDG WAS MADE WITH 'CRASH EQUIP' ON STANDBY. WE CLRED THE RWY AND BROUGHT THE ACFT TO A STOP WAITING FOR THE 'TRUCK' TO COMPLETE A VISUAL WALKAROUND. I WAS NOT AWARE THAT THESE TRUCKS ARE EQUIPPED WITH INFRARED (HEAT) MONITORS. VERY IMPRESSIVE!! WE WERE ADVISED THAT A TIRE ASSEMBLY WAS WARM WITH MINOR SMOKE. 'TRUCK' ASSISTED US TO THE GATE AFTER 'AFTER LNDG' CHKLIST COMPLETE AND FA'S ADVISED OF SIT. ONE COMMENT REGARDING CTL. IT WAS BANK TIME FOR PIT AND BUSY TO SAY THE LEAST. WE ASKED FOR A EXTENDED FINAL AND GOT TURNED IN TIGHT; TWICE. WE HAD NOT CONFIRMED WITH HIM WE WERE READY UNTIL THE 2ND APCH BEGAN AND APPEARED IT WAS DIFFICULT TO WORK US IN; EVEN THOUGH WE HAD EMER AUTHORITY. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR ADVISED TYPE ACFT AS B737-500. MAINT LATER ADVISED THAT SPLIT FLAP PROB WAS ATTRIBUTED TO A FAULTY GAUGE. RPTR'S OTHER PROB WAS ATC. HE ADVISED THAT HE WOULD NEED TO BE POSITIONED WHERE HE COULD TAKE THE APPROX 10 MIN CHKLIST FUNCTION. DURING THE FIRST VECTOR FINAL; THE FLC HAD ASKED FOR AN EXTENDED DOWNWIND; BUT WAS VECTORED FOR A SHORT TURN IN; REQUIRING THE GAR.THE SECOND TIME; THE FLC RECEIVED THREE FREQ CHANGES; TWO ALT CHANGES AND TWO REDUCED SPEED CHANGES. THE RPTR ADIVISED THAT THESE ADDITIONAL DISTR'S ADDED TO; AND CAUSED SIGNIFICANT COCKPIT WORKLOAD.