some vets will be ok with you carrying on, but it's a bit of a difficult one as in order to sign the certificate to have it done, the dates must be right, and if they aren't then technically speaking the horse is NOT vaccinated, and the vet has signed the certificate falsely. As the vaccination certificate is technically a legal document, for a vet to put their signature on it when the dates are not within the guidelines is actually asking the vet to falsify a legal document. It's a bit of a minefield!
In terms of the horse, as tina says, it doesn't really matter, but for showing it's vital that the dates are correct or you will be refused entry. Some livery yards are particular about it too. You would have to start again from scratch and though it's expensive, you also need to consider that if you sell him on again, you will be selling on a horse that doesn't really have an up to date vaccination record, even if it's a few years down the line and he's been having them every year, until the primary course has been done again it's invalid!