Dear Zoe,
I hear the dilemma you feel in balancing your relationship with your colleague on the one hand and doing the ethical thing—abiding by the rules—on the other. The fact that your colleague confessed his hiding of past incidents to you suggests he trusts you. Have you considered asking him to confess to his supervisor himself, or at least be willing to report future errors? You may be able to influence and persuade him to do so.
If he still refuses to do so, then you will need to prayerfully consider whether to blow the whistle on him or not. Some factors to consider: (1) How detrimental will it be to the organisation or others if this colleague continues to hide future errors? (2) Does the organisation treat such reporting of errors fairly, i.e. not be overly harsh and punitive? Your willingness to do so yourself suggests it is not. (3) How important is your relationship with your colleague to you? Are you willing to risk his displeasure and retaliation in order to do what you think is right? Pray for the Lord to grant you discernment, and also the wisdom and courage to do what he leads you to do.