Is the Scheduler passing parameters into the stored procedures? Are any values defined differently depending on the execution steps? If so, I would start with checking those values. Since the two do not error in stand alone mode, I would think the errors are not initiated from a database query. But, do not eliminate any option from trouble-shooting.
If possible, use dbms_output to write out all variable values at various stages within the code. PL/SQL doesn’t have wonderful debugging tools, so writing out values is crude but helpful. Maybe someone else has some better tools to recommend.
Stored procedure may be having the date conversion functions like To_Date and To_Char. Please verify the NL_DATE_FORMAT in NLS_ENV column of DBA_JOBS , May be date conversion done in stored procedure is not compatible with the NL_DATE_FORMAT in NLS_ENV column of DBA_JOBS. So job is showing error. Recreate the job with proper NL_DATE_FORMAT.