No, don't amend your return.
The odds are that the IRS will detect the incorrect SSN when cross-checking against its name control database. They'll almost surely make the correction, and you'll never be contacted about it.
If they catch the error but can't correct the SSN, and the loss of your son's dependency results in a change in your refund or balance due, you'll be notified, and you can then address the issue.
The same logic most likely applies to your state return, so don't amend that one, either.
