CAPT OF AN MD88 OVERSHOT ASSIGNED ALT DURING DEP DUE TO DISTR OF THE FLT DIRECTOR NOT RESET TO THE NEW HDG ASSIGNMENT.

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WE DEPARTED DCA ON RWY 18 WITH A CLRNC TO INTERCEPT THE DCA 185 DEG RADIAL AND MAINTAIN 5000 FT. THE CAPT WAS HAND FLYING THE AIRPLANE WITH FLT DIRECTOR COMMANDS. DURING THE LAST 1000 FT OF THE CLB WE WERE ISSUED A L TURN TO THE E. I SELECTED THE HDG BUG TO THE NEW HDG; BUT DID NOT CANCEL THE PREVIOUS FLT DIRECTOR COMMAND TO INTERCEPT THE 185 DEG RADIAL. WHILE IN THE TURN; THE FLT DIRECTOR CAPTURED THE 185 DEG RADIAL AND DISPLAYED THE CORRESPONDING COMMAND. BOTH OF US WERE MOMENTARILY DISTR WHILE WE TRIED TO RECONCILE THE APPARENTLY CONFLICTING INFO WE WERE RECEIVING FROM THE FLT DIRECTOR (IE; THE ROLL BAR INDICATING A R COMMAND WHEN I HAD SELECTED A HDG TO THE L). IN ADDITION; WE WERE EXPERIENCING LIGHT TO MODERATE TURB DURING THE CLBOUT FROM LATE AFTERNOON THERMALS. AT 5300 FT WE HEARD THE ALT AURAL WARNING. THE CAPT IMMEDIATELY ARRESTED THE CLB AND DSNDED TO 5000 FT. THE MAX ALT REACHED WAS ABOUT 5350 FT. THERE WAS NO TFC CONFLICT OBSERVED ON TCASII. ATC DID NOT QUERY US; AND JUST AS WE WERE LEVELING AT 5000 FT; ISSUED A CLRNC TO CLB. THE PF WAS PERHAPS DISTR BY THE TURB DURING THE CLBOUT; AS WELL AS THE APPARENT FLT DIRECTOR DISCREPANCY JUST AT THE TIME WHEN HE WOULD NORMALLY BE LEVELING OFF. THIS KIND OF SIT CAN BE AVOIDED IN THE FUTURE BY THE PF CONCENTRATING ON ACFT CTL (ESPECIALLY WHILE HAND FLYING); AND HAVING THE PNF RESOLVE ANY DISCREPANCIES. ADDITIONAL VIGILANCE BY THE PNF IN MONITORING THE FLT PATH SHOULD ALSO BE EXERCISED; PARTICULARLY DURING HIGH WORKLOAD PERIODS SUCH AS THIS.