FLC OF B757 HAS LEADING EDGE FLAP DISAGREE INDICATION ON DSCNT FOR APCH. RECEIVING CLRNC FOR A HOLD TO TROUBLESHOOT THE PROB; THEY NEGLECT TO REPROGRAM THE ALT. ALTDEV OCCURS.

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ON ARR TO EGE WE WERE E OF RLG AT 15000 FT SLOWING THROUGH 220 KTS FOR 210 KTS WHEN FO; FLYING; CALLED FOR FLAPS 1 DEG. EICAS DISPLAYED TRAILING EDGE FLAP DISAGREE MESSAGE. I FELT PRETTY SURE WE WOULD NOT COMPLETE THE APCH TO EGE AND ASKED ZDV IF WE COULD HOLD AT RLG TO SORT IT OUT. THEY CLRED US TO HOLD N AT 15000 FT. AS WE WERE AT 15000 FT WE HAD ALREADY SET 13100 FT IN THE ALT WINDOW FOR THE NEXT LEG OF THE APCH. BY THE TIME WE GOT HOLDING INSTRUCTIONS WE WERE NEARLY OVER RLG AND THE FMC WOULD NOT ACCEPT A HOLD. I WAS IN VOR RAW DATA AND SET THE INBOUND RADIAL AND TOLD THE FO TO START OUT IN RAW DATA AND I WOULD SET HOLDING. AFTER PASSING RLG I WAS ABLE TO SET THE HOLD BY DIRECT INTERCEPT RLG; THEN SETTING UP THE HOLDING PAGE. THE FO SET EVERYTHING BACK UP AND AS WE PATTED OURSELVES ON THE BACK FOR OVERCOMING AUTOMATION AND GETTING OURSELVES SET TO SOLVE OUR FLAP PROB DEN ASKED OUR ALT AND THEN CLRED US TO 14000 FT. AS SOON AS WE HAD CROSSED RLG AND HEADING SELECTED OURSELVES INTO THE HOLDING PATTERN WITH VOR RAW DATA; VNAV CONTINUED TO OPERATE AS ADVERTISED AND BEGAN A SLOW DSCNT TO 13000 FT; OUR NEXT ALT. DEN WASN'T UPSET BUT IT WAS A SOBERING REMINDER THAT IF YOU KILL THE AUTOMATION MAKE SURE YOU KILL IT ALL.