The legal mechanism used to enforce orders in a divorce decree is a Motion for Rule to Show Cause, better known as a contempt.
If he was ordered to pay something in the decree and failed to, then he can be found in contempt of court.
If he is found in contempt, then usually the court will order him to reimburse you for your attorney fees and can make his life a living hell in a variety of wasy.
The problem is that if he files a bankruptcy petition and lists both you and the creditor to whom the debt is owed, he's likely going to get the decree obligations tossed, leaving you on the hook.
If the payments are late, that will show up on your credit report as such.
The agencies report only fact -- was the payment late or was it not. They don't delve into who was "right" and who was "wrong."
If you believe it is his fault that there are late payments or missing payments, you can write a statement to each of the three credit bureaus, explaining your situation and asking that the statement be provided to anyone who is seeking access to the credit report.
Your scenario is so common in divorces, unfortunately, when the debts are not classified as child or spousal support or maintenance.
Hope this information helps. Best of luck to you!