Twins file number is lower than Obama who was born the day before. According to the proper sequence Obama should've had a lower number,since he was born the day before. You answered your own question. In theory, the numbers should be assigned in order of birth, but who knows what went on in the office, how the forms were stacked and sorted (or mis-sorted) before being stamped with the file number. I don't see this as an issue, unless you expect absolute perfection out of a government office in 1961 (or any time for that matter).
Several possibilities:
1. They went in an in box in birth order but filed from the top of the pile down.
2. More than one person was filing that morning.
3. Some klutz dropped a stack of papers and picked them up out of order.
I don’t see why this is a big deal.
It seems that the same person wrote the date of the mothers’ signatures “8-7-61”. It certainly was not written by the mother of the twins.
Perhaps it was written by a hospital clerk who only worked several days a week, going from room to room to collect the signatures as part of the filing process. The blank forms could have been attached to charts when the mothers entered the labor/delivery process. The births are less than 24 hours apart. I don’t attach any significance to the lack of continuity of these births.
Who were babies 10639 and 10640? Will we see them on reality tv someday?
I wouldn't even call this a clerical error. These things pile up in a 9 to 5 clerks in-box in roughly the order in which the kids were born as nurses wonder up and down the hall; the registrar then pulls them out beginning with the one on top, assigns it the next number in sequence, and proceeds to fill in whatever he/she must add. Thus little Baracky's paperwork was below several others' who were born later, but received earlier registration numbers.
I'm an agnostice about the BC, but I don't think this point is particularly important. I've just worked as a clerk in a military hospital and know how these things were done in 1970, anyway.