A B737-700 ASSIGNED THE SLC WAATS ONE RWY 16R WAS CHANGED TO RWY 16L AFTER SLAGG. LNAV DISCONNECTED DURING REPROGRAMMING AND WAS MISSED BY THE CREW; CAUSING A HDG DEV.

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WE WERE IN LNAV ON THE WAATS ONE ARR INTO SLC. AFTER PASSING SLAGG INTXN WE WERE TOLD TO EXPECT RWY 16R. WE HAD PREVIOUSLY BRIEFED AND PROGRAMMED RWY 16L AND QUICKLY SWITCHED APCH PLATES; CHANGED RWYS IN THE FMC AND ILS FREQS. DURING THE RAPID SERIES OF CHANGES WE WERE BOTH MAKING; I FAILED TO CALL FOR FO CONCURRENCE WITH THE PROGRAMMING CHANGE I HAD MADE IN SWITCHING RWYS IN THE FMC. THE CHANGE OF RWYS IN THE FMC KNOCKED US OUT OF LNAV AND I DID NOT SPOT IT UNTIL WE HAD OVERSHOT THE TURN AT QUIPA. WE WERE CORRECTING BACK WHEN APCH CALLED US AND ASSIGNED A HDG. LATER; WHILE TURNING ON TO FINAL; AFTER HAVING BEEN CLRED FOR THE VISUAL TO RWY 16R; APCH CALLED US AND TOLD US TO START OUR TURN ON TO FINAL (APPARENTLY OUR TURN HAD NOT YET REGISTERED ON HIS SCOPE). AFTER LNDG WE WERE TOLD TO CONTACT APCH. THE SUPVR ASKED ME THE REASON FOR THE OVERSHOOT AT QUIPA AND ALSO ASKED US WHY WE HAD OVERSHOT THE FINAL. I EXPLAINED AND APOLOGIZED FOR THE OVERSHOOT AT QUIPA; AND ALSO EXPLAINED THAT WE HAD NOT OVERSHOT FINAL (WE HAD IN FACT ROLLED OUT RIGHT ON THE EXTENDED CTRLINE; CONFIRMED VISUALLY; BY THE ILS AND THE MAP DISPLAY). THE SUPVR SAID HE HAD NOT REVIEWED THE TAPES; BUT THAT THE CTLR HAD BEEN CONCERNED ABOUT TFC ON THE PARALLEL APCH. THE SUPVR INDICATED THAT NO FURTHER ACTION WOULD BE TAKEN. ASKING FOR THE RWY TO EXPECT EARLIER. HAVING THE CONCURRENCE OF BOTH PLTS ON ANY PROGRAMMING CHANGE AND CONFIRMING THAT THE LNAV MODE IS STILL ENGAGED AFTER A CHANGE WOULD HAVE PREVENTED THIS SITUATION.