Is what was narrated about Al-Mughirah ibn Shu'bah—may Allah be pleased with him—regarding his marriage to seventy women and divorcing them without a Sharia-compliant reason, then gathering four of them and divorcing them all at once, authentic? And is it permissible to describe his action as a mistake?

The marriage of Al-Mughirah ibn Shu'bah, may Allah be pleased with him, to seventy women or more is well-established about him. This is commendable for him, as it indicates his full virility, protects women, seeks children who would be mujahideen, and increases the Muslim nation. The Prophet of Allah, Solomon, peace be upon him, also did similarly.

As for the upbringing of his children, the Companions raised their children in the best possible manner, and the society at that time was virtuous, which aided in this.

What is mentioned about him divorcing his wives without reason is not established about him, and its chain of narration is weak. One must have a good opinion of the Companions, as generally they do not divorce except for a reason, and they do not disclose private reasons for divorce.