Cimrman si nesl v osobních dokladech záznam "strůjce nepokojů."
The main verb is "nesl si" 3sg. past tense form of nést "to be carrying (on foot)"
The subject is the nominative Cimrman. The direct object in the acc. is záznam "entry, title". V osobních dokladech is a preposition phrase and would not qualify for the direct object.
Strůjce nepokojů "the builder of unrests" is a specific name for the title in Cimrman's personal documents. Since it is a name preceded by a generic noun "záznam," "strůjce" should remain in the nominative case and nepokoje (nom. sg. nepokoj) in the genitive case to mean "of unrests." (Similar example: Četli jsme časopis Vlasta. 'I read the magazine Vlasta' where "Vlasta" is a concrete name for the generic noun "časopis")
The form is therefore correct as it is.