As harmful this error was to you, I can't think that in the long run, it would be worth while to try to sue them for their error. Even if they had liability, (and I offer no opinion on that), the amount of money you could win would never equal the time, expense and trouble of the suit. EDD's lawyers' fees don't come out of one cash strapped individual's pocket. I just don't see this leading anywhere. But maybe an attorney with specific experience on EDD issues will answer you.
Mr. Dinday makes an excellent point about the feasibility of a civil action against the EDD. In addition, the EDD enjoys a number of potential immunities which may bar liability for money or damages even if you could prove the EDD was negligent or at-fault. You run the risk that you may have to pay EDD's costs and attorney's fees if you file and maintain a civil action for money or damages where the EDD is immune from liability.