so sorry for your loss.
on the death cert. date-contact the mortuary and find out which government office you need to contact (they may be able to give you a specific contact name and number which will save you dealing with multiple calls).
on who to send the corrected ones to-did your ds have any kind of assetts? did he have any debt? did he leave a will? this is primarily where the death certs come into play.
i lost a sibling recently, he left no will, and had no spouse/children. therefore all his assetts will revert to my mother. in her case, some of his assetts had beneficiaries named so death certs will be used for those individuals to make application to receive the assetts. in the case where there's no named beneficiary or pod (pay on death) like his bank accounts, car and a storage locker-then if his estate was'nt subject to probate, my mom would have to wait the number of days whoever held the assett (or controlled it's title-like the dmv for his cars) required, do the necessay affadavit and provide a death certificate.
when another family member passed recently, and dh had to handle the estate, we had to provide death certificates to: dmv, bank, former employer (for pension on account), life insurance companies, cell phone company (she had a new contract, and to cancel service they required a death cert.), storage facility (they kept the thing locked for 90 days and we had to continue paying storage just in case there was anything of value in it-which there was'nt), auto/renter's insurance carrier (to get refund of pre-paid amounts), and one for the credit bureau.
with the credit bureau it was for us to be able to see where the person had open accounts-that way we could notify to close them, and ensure there were'nt any kind of monthly charges that were set up to keep posting (which we found was the case with the person's internet provider).