A B737-300 EXPERIENCED A FLAP ASYMMETRY AND OTHER SYS ANOMALIES BEFORE LNDG. AN EMER WAS DECLARED.

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WHILE CONFIGURING FOR LNDG ON APCH INTO ZZZ; WE HAD AN ASYMMETRICAL TRAILING EDGE FLAP PROB WITH A ROLL TENDENCY. WE EXECUTED A GAR. WE CONTACTED DEP AND EXPLAINED THAT WE HAD A FLAP PROB AND TO PLEASE KEEP RADIO CALLS TO A MINIMUM. WE ALSO REQUESTED THAT THEY KEEP US CLR OF TERRAIN BECAUSE IT WAS AT NIGHT. APCH CTL SENT US TO ABC TO HOLD AT 6000 FT ON A NON PUBLISHED HOLDING PATTERN. THE AUTOPLT WOULD NOT ENGAGE; AND WE HAD SEVERAL RADIO FREQ CHANGES. THE MCP ALT SELECTOR WOULD CHANGE FROM SELECTED ALT TO FL500. I RESELECTED THE ALT AND A FEW MINS LATER IT CHANGED BACK TO FL500; ADDING TO THE WORKLOAD. THE AIRSPD CURSOR WAS ALSO INOPERABLE. WHILE READING QRH FOR AN ASYMMETRICAL FLAP; 1 NEEDLE INDICATED 1 DEG AND THE OTHER INDICATED 2 DEGS. WE SELECTED FLAP 1 DEG FROM 5 DEGS AND NO CHANGE WITH FLAP INDICATOR. DURING THIS TIME; WE CONTACTED OPS TO INFORM THEM THAT WE HAD A FLAP PROB. WE ALSO INFORMED THE FLT ATTENDANTS AND MADE A PA TO PAX. WE RETURNED TO CHKLIST AND AFTER ARMING ALTERNATE FLAP SWITCH; WE DISCOVERED BOTH FLAP INDICATOR NEEDLES AT 1 DEG. WE STOPPED AND REFERRED TO PAGE XXX THINKING SOMETHING WAS WRONG WITH LEADING EDGE DEVICES. WE HAD AN MEL AMBER LEADING EDGE LIGHT PLUS OVERHEAD PANEL INDICATING #3 SLAT IN TRANSIT. THIS WAS CONFUSING BECAUSE I HAD FORGOTTEN ABOUT MEL FOR A MOMENT. WE THEN NOTICED THAT THE FLAP INDICATOR HAD CHANGED TO 1 DEG AND 10 DEGS RESPECTIVELY. WE THEN RETURNED TO QRH AND COMPLETED CHKLIST. WE CONTACTED APCH AND DECLARED AN EMER. DURING APCH; ANOTHER CARRIER WAS LNDG. TWR ASKED THEM TO MAKE AN EARLY TURNOFF. THEY REPLIED THAT THEY WOULD 'TRY.' TWR THEN APPROVED US FOR S-TURNS; WE REPLIED UNABLE. ABOUT 200 FT WE GOT A STICK SHAKER WHILE ON SPD. WE MADE A NORMAL TOUCH LNDG WITH FULL LEADING EDGE DEVICES AND TRAILING EDGES AT 1 DEG. TARGET SPD WAS 156 KTS. LNDG WAS UNEVENTFUL. DURING DEPLANEMENT; MOST PAX WERE SAYING THANK YOU FOR A SAFE LNDG; BUT ONE SAID IT WAS HIS SECOND MAINT PROB TODAY ON COMPANY AND HE WOULD NOT RIDE ON US AGAIN. THIS WAS DISTURBING TO ME. I DID NOT GET HIS NAME. WHILE ON GND IN ZZZ; WE CONTACTED DISPATCH TO EXPLAIN THE SIT. THERE WERE 2 DISPATCHERS ON THE TELEPHONE. ONE SAID HE WAS THE SUPERVISOR. THE SUPERVISOR SEEMED UNHAPPY AND WANTED TO KNOW WHAT WAS GOING ON; WHY AFTER 1 HR 30 MINS TO ZZZ AND NOT ON THE GND. I PERCEIVED HIS COM AS BEING ADVERSARIAL. I TRIED TO EXPLAIN THAT OUR WORKLOAD WAS EXTREME; WITH MOUNTAINOUS TERRAIN; AT NIGHT; NO AUTOPLT; AND A VERY CONFUSING FAILURE; THAT I HAD A BRIEF MOMENT TO NOTIFY ZZZ OPS; FLT ATTENDANTS; AND PAX. SAFETY OF FLT WAS MY PRIORITY.