Is a person considered to have erred if he was late for Jumu'ah prayer and did not hear the khutbah, then prayed four rak'ahs with the intention of Dhuhr, while others who also missed the khutbah prayed only two rak'ahs?

Whoever catches one rak'ah with the Imam from the Friday prayer has caught Friday prayer. He should add another rak'ah to it and not pray four, because attending the khutbah is not a condition for the validity of the follower's prayer.

If a worshiper prays four rak'ahs with the intention of Dhuhr and does not pray two rak'ahs with the Imam with the intention of Jumu'ah, it is safer for him to repeat the Dhuhr prayer due to the scholarly disagreement on the validity of praying Dhuhr before the time for Jumu'ah has passed.