I have my grandmother's short birth certificate. It gives the date of her birth and the date on which the birth was registered. This latter date fell in the following quarter, which was also in the next year.
At the bottom, it gives the Registration district - and the sub-district.
Mistakes did occur when the main GRO index was compiled but if that fails, the local office should be able to track down the entry from the information on the short certificate e.g. entry 72 in Book No 32, plus the name and the dates.
Nell