I just filed and realized that my husband's W2 has an incorrect SSN. He's going to ask his work to fix this, but my Federal return is already filed. Any concerns?

Please see the information provided here for assistance with your husband's incorrect W-2 form. If you receive a corrected Form W-2 after you filed your return, and the information differs from the information reported on your return, you must amend your return by filing Form 1040-X, Amended U.S. Individual Income Tax Return.

Thank you! Does this need to be done for state taxes returns as well? (California)

If the IRS does not reject the return and nothing else is different but the SS number on the W-2, I would not amend it.