I'm an occasional lurker but just saw this post.
You need to take some sort of proof (death cert, notarized doctors records w/ date of death noted, in some cases some will take records from the cemetery or funeral home) to your local social security admin office.
In a lot of instances they will already have the correct date but the SSDI will have (and continue to have) the incorrect information, as it's compiled by a 3rd party and different places online all have different updates. I know the SSDI on Rootsweb allows you to post a sticky note on a particular person so anyone who does look up that record can note the correct information.