I don't know how the information of the data on old birth certificates in the US was collected, stored, and later perhaps even photocopied/scanned on microfilm, or some other media. I can understand how the date of birth on an old birth certificate got wrong. What I have seen of old birth certificates, they were usually pre-printed documents, with space where additional info such as name, date of birth, and so on was filled in. Back in the mid-1940 the added info could either be written by hand, or typed in. Back then the typewriter tapes were made of fabric, and reused, often for a long time, and faded out letters/numbers could be difficult to interpret, especially from a photocopied original. It might be difficult to see the difference between a '5' and a '6', maybe even with handwritten ones.