Pretty odd for IRS to accept an incorrect SSN on a return, it would have needed to belong to someone else with the same first 4 letters of their last name (I guess if its a common last name, it can happen)....
Im not sure an amended return would do anything for this situation. I think you may be stuck waiting to see if IRS sends any notice about it.
This is why its so important for the client to review the return prior to filing, and they should always verify the name and SSN is correct on the 8879.
If it just happened to be a legitimate SS and last name of another taxpayer, then as far as the IRS is concerned your client has not filed. I would wait at least 3 weeks, then check IRS where is my refund, and if there is no record I would file your clients return with correct SS number. Be sure to let your client what is going on.
I agree that the social would have to match the name for the federal to not get rejected. However, the state doesn't always work that way.
If either fed/state was filed incorrectly. I would send the amended return with the explanation of "Clerical Error" and state the original filed social and the correct one - enclose an "As originally filed" return copy as well as an "As amended" return copy with the 1040-X or other state Amended form.
Seem like amended would have to be paper filed as Intuit software wont let you alter the SS# once it has been transmitted.