The handwritten memo seems pretty odd, as if added after the fact, since no child was mentioned on the other form of the same date. A previous memo was typewritten. Would an inspector have time to go track down information about the wife and child and file it the same day ... and especially when other sources say she was already in Washington before the end of August?
Lately I have been focused on researching documentary evidence to support the correct understanding of the term of art "natural born citizen" and I have not been looking into Obama's origins as much as I used to. I know that a lot of people have poured over the INS documents for Barack Sr, but I have only given them a cursory look, and have focused on some aspect of one of them when it has been brought to my attention by others.
What this means is that I am not currently in a position where I can offer an informed opinion on this peculiarity you have mentioned, but off the top of my head, it would seem unlikely that an inspector could do very much research the same day. Alternatively, I would suggest that this person may have been familiar with the case from other interactions with these people, perhaps not all of which was noted down on paper. (or if so, are on documents we haven't seen yet.) In any case, I will keep your point in mind, and perhaps a sensible answer will eventually appear.
... and especially when other sources say she was already in Washington before the end of August?
As far as I know, the only source placing her in Washington in August is Susan Blake. Is there another source placing her there at that time? (The University Records were determined to have been reported incorrectly. When the error was discovered they place her there in September, not August.)