My dad too. He was a twin and they got his sister’s date right and his wrong. He died young, so I don’t know if it affected him, but it is still affecting me and he was born in 1911. I have to prove his DOB by going to the 1920 census which wasn’t available at the time I needed the information. It is available now, of course, but it doesn’t seem to matter any more.
I’d never heard of this type of thing until my dad had to deal with it.