Error: applying the explicit-noun rule to every sentence with a dual subject.
Correct distinction: «ضَرَبَ الزَّيْدَانِ» has an explicit subject, so the verb is singular; «الزَّيْدَانِ ضَرَبَا» has a dual subject pronoun attached to the verb, so the verb is dual.
Error: assuming every grammatically feminine noun requires feminine agreement.
Correct: the rule differs for real versus non-real feminine subjects and according to whether separation occurs.