It is impossible for me to say whether closing the joint accounts will have any effect on your credit score without knowing more about your credit history. However, the possible impact on your credit score is the least important reason why you and your ex-spouse should close any remaining joint accounts you two share.
The recent recession, drop in housing prices, and high unemployment rate has pushed many people into foreclosure, default on credit card debt, and bankruptcy. Both you and your ex-spouse may have jobs and a sound financial footing today, but in life there are few guarantees. The fact that you two are no longer married gives you limited opportunities to influence the behavior of your ex-spouse (and vice-versa). If your ex-spouse (or you) decide to push the balance of your joint account(s) to the limit and then default on the payments, neither the credit card companies or the courts will care that you two divorced many years ago. A joint account is a joint account, and if one joint account holder refuses to make a payment the other joint account holder is contractually bound to.
Closing an account with a long positive payment history can have a negative impact on your credit score. However, even if there were a slight benefit to keeping the accounts open, I do not think that the benefits outweigh the potential risks associated with having a credit card account for which you are liable out of your control.
I encourage you to review your credit reports to verify that all information being reported is accurate and up-to-date. You can request a copy of your credit report from each of the three major credit bureaus -- Experian, Equifax, and TransUnion -- by visiting AnnualCreditReport.com. Once you have received copies of your reports, you should carefully review them to make sure that all listings, especially the listings appearing in the "derogatory" category, belong to you and are being reported correctly. Credit reports are notoriously inaccurate, with consumers frequently finding listings of derogatory accounts that never belonged to them or that were paid off years ago.
If you find any inaccurate listings, you should dispute them with the appropriate credit bureau. See the Federal Trade Commission document FTC Facts for Consumers: How to Dispute Credit Report Errors for more information. Clearing up inaccurate derogatory accounts may significantly improve your credit score, depending on the number of inaccurate listings you find on your reports.
To learn more about credit scores, see the Bills.com resource FICO Score Calculation.
I hope this information helps you Find. Learn & Save.