Even if your divorce decree specifies that your spouse is responsible for particular debts incurred during a marriage, your credit score may still be at risk if your spouse does not make timely payments on accounts that are under your name also.
The problem is that the parties that extended the credit in the first place are not parties to the divorce and they are not concerned with how the debt was divided in your settlement. In the eyes of your creditors, if there are shared accounts or debt that is considered to be joint, non payment on those accounts during or after the divorce may affect the credit standing of both spouses, not just the one deemed responsible by the divorce decreee.
Faced with this financial limbo, what can you do? Ideally, the spouses will agree to pay off and close joint accounts or convert them to individual accounts where possible. If this approach is not an option, it may be possible to set up online access to the account so that the spouse who is not responsible can at least review payment history and issue reminders to their ex if they see delinquent activity.
If your ex is unwilling or unable to keep up with payments on joint accounts despite a court order, then it boils down to whether you choose to make the payment to fend off negative data on your credit report or take the hit. If it comes down to you making the payments on behalf of your spouse, you may be able to approach the court for recourse.