FLC OF MLG HAS SLAT DISAGREE LIGHT ACTIVATE. NO CTL PROBS EXIST SO THEY CONTINUE THE APCH AND LNDG. ON ROLLOUT THEY DISCOVER THEY HAVE NOT CONTACTED TWR FOR LNDG CLRNC.

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WE HAD BLOCKED OUT OF MSP 45 MINS LATE FOR STL DUE TO FLOW CTL AT STL BECAUSE OF LOW CEILINGS AND VISIBILITY. THE FO WAS FLYING THE LEG. THE FLT WAS NORMAL UNTIL THE APCH AT STL. AFTER SLATS AND FLAPS 5 DEGS HAD BEEN SELECTED; THE SLAT EXTEND LIGHT BEGIN TO FLICKER AND THEN WENT OUT. THE SLAT DISAGREE LIGHT CAME ON. AT THIS TIME; WE WERE IN THE MIDDLE OF A LINE OF ACFT BEING VECTORED BY APCH TO RWY 30R AT STL. WHILE THE FO FLEW THE ACFT; I STARTED THE SLAT DISAGREE PROC. ALTHOUGH THE PROB APPEARED TO BE A LIGHT OR SWITCH PROB (WE HAD NO ADVERSE ROLL INDICATING THE SLATS WERE OUT EVEN) WE INCREASED SPD IN COORD WITH APCH IN ORDER TO FOLLOW THE CHKLIST. DURING THIS TIME; I HAD A FLT ATTENDANT WHO KNEW WHAT THE EXTENDED SLATS LOOK LIKE MAKE A VISUAL CHK. HE CONFIRMED THAT THE SLATS WERE EXTENDED. AT THIS POINT; WE WERE CLRED FOR APCH. WE ELECTED TO CONTINUE AND SLOWED TO 170 KTS TO FIT IN THE APCH SEQUENCE. WHEN FLAPS 15 DEGS WERE SELECTED THE SLAT EXTEND LIGHT CAME BACK ON AND THE DISAGREE LIGHT WENT OUT. WE WERE APCHING THE OM AND OUR FULL ATTN SHIFTED BACK TO THE INST APCH. THE REST OF THE APCH AND LNDG WAS NORMAL. WHEN TURNING OFF THE RWY; THE FO WENT TO SELECT GND CTL AND THAT'S WHEN WE REALIZED THAT WE HAD NOT SWITCHED AND CALLED THE TWR FOR LNDG CLRNC. APCH USUALLY SWITCHES YOU TO TWR RIGHT AFTER THE CLRNC FOR APCH. WITH THE INCREASED WORKLOAD OF THE SLAT PROB; NEITHER OF US EVEN REMEMBERED HEARING APCH SWITCH US. IN THE FUTURE; I WILL DISCONTINUE THE APCH; SOLVE THE PROB; AND THEN CONTINUE IN ORDER TO LOWER THE WORKLOAD.