ACFT EQUIP PROB DISTRACTED A FLC FROM FLYING THE AIRPLANE. ALTDEV ALT OVERSHOT.

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A HVY (FERRY FLT) TOOK OFF FROM SAN ANTONIO ARPT FROM RWY 12R; IN VMC. I WAS FO PERFORMING RADIO COM AND THE CAPT WAS THE PF. AFTER TKOF; WE WERE SWITCHED OVER TO DEP FREQ AND RECLRED TO CLB TO 13000 FT. DURING CLB; WHILE FLAPS AND SLATS WERE RETRACTED; THE KRUGER FLAP LIGHT WAS STILL FLASHING; INDICATING DISAGREEMENT BTWN THE FLAP/SLAT HANDLE AND KRUGER FLAP POS. FE HAD THE ABNORMAL CHKLIST READY AND I BEGAN WORKING WITH HIM THROUGH THE CHKLIST. WE ALSO REACHED 12000 FT AND I CALLED 1000 FT TO LEVEL OFF; AND AGAIN TRIED TO FINISH THE CHKLIST. AFTER A FEW SECONDS; I HEARD ALT ALERT SOUND AND REALIZED THAT CAPT HAD OVERSHOT THE ASSIGNED FLT ALT. I IMMEDIATELY INFORMED THE CAPT AND HE ALSO CORRECTED THE FLT ALT IMMEDIATELY BACK TO 13000 FT. THE AIRPLANE WAS VERY LIGHT AND IN CLB THRUST PWR SETTING. I BELIEVE IF THE CAPT HAD ENOUGH EXPERIENCE ON L OR EVEN R SEAT OF A HVY TRANSPORT JET; THIS WOULD HAVE NEVER HAPPENED. I NEVER HEARD ANY INSTRUCTION FROM THIS CAPT; HE NEVER TALKED TO US REGARDING CREW MEMBERS COURSE OF DUTY; SPECIFICALLY WHO WOULD FLY THE AIRPLANE AND WHO SHOULD TAKE CARE OF ABNORMAL CHKLIST WITH THE FE. SUPPLEMENTAL INFO FROM ACN 319340: WE WERE FERRYING AN ACFT THAT HAD BEEN SITTING FOR SEVERAL MONTHS. SEVERAL FAILURES OCCURRED AT THE SAME TIME INCLUDING A MOMENTARY FAILURE OF THE CAPT'S SIDE VOR/HSI AND KRUGER FLAPS WOULD NOT RETRACT. IN THE CONFUSION; I FAILED TO LEVEL OFF; AND WE WENT TO 13800 FT.