AN ACR FO COMPLAINS THAT THE AUTOPLT DID NOT LEVEL THE ACFT AS COMMANDED.

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PROB AROSE WHEN THE AUTOPLT DIDN'T LEVEL OFF AT FL240. IT WAS DISCOVERED WHEN THE 'ALT' WARNING SOUNDED PASSING FL236. SWITCHED TO MANUAL CTL AND RETURNED ACFT TO FL240. LOWEST ALT WAS FL234. CONTRIBUTING FACTORS WERE: 1) VECTORED OFF COURSE FOR SPACING ON ARR; AND AFTER FMA DISPLAYED 'ALT CAP;' I DIVERTED MY ATTN TO CONSTRUCTING A NEW DSCNT PROFILE INTO FMS. 2) DSCNT AIRSPD WAS 320 KTS; LEVEL OFF AIRSPD FOR CRUISE AT FL240 WAS 250 KTS. DURING SLOW-DOWN; THE AUTOPLT TRIM COULD NOT KEEP UP; SO ACFT COULD NOT HOLD ALT. WHEN SWITCHED TO MANUAL; I NOTICED A LOT OF NOSE DOWN TRIM. HUMAN PERFORMANCE CONSIDERATIONS: IT IS VERY EASY TO PUT TOO MUCH CONFIDENCE IN ACFT AUTOMATION RESULTING IN LACK OF PROPER MONITORING DURING EVENTS SUCH AS LEVEL-OFFS AND COURSE INTERCEPTS. IT IS IMPORTANT TO ALWAYS FIND THE PROPER BAL FOR USING/NOT USING AUTOMATION AND PROGRAMMING IT. WE HAVE NOTICED IN SOME MD-88'S THAT THE AUTOPLT TRIM HAS TROUBLE KEEPING UP WITH AIRSPD AND CONFIGN CHANGES; AND I BELIEVE THIS IS THE PRIMARY REASON FOR THE ACFT NOT LEVELING OFF AT FL240 WITH THE AUTOPLT ON. THIS SHOULD HAVE BEEN PREVENTED WITH BETTER MONITORING OF THE LEVEL OFF AND ENSURING THE ACFT WAS STABLE AT FL240 BEFORE DIVERTING ATTN TO OTHER DUTIES.