From this:

Responding to a Freedom of Information Act request, the State Department has released passport records of Stanley Ann Dunham, President Obama's mother – but records for the years surrounding Obama's 1961 birth are missing.

The State Department claims a 1980s General Services Administration directive resulted in the destruction of many passport applications and other "non-vital" passport records, including Dunham's 1965 passport application and any other passports she may have applied for or held prior to 1965.

Destroyed, then, would also be any records shedding light on whether Dunham did or did not travel out of the country around the time of Barack Obama's birth...

There's much more at the link, including a heretofore unknown name for Barack Obama which was used in relation to his stay in Indonesia: "Saebarkah". Not knowing Indonesian languages leaves me at a disadvantage, but that sounds like some sort of title ("sae") plus a possible more Indonesian version of "Barack". Although that could just be a coincidence and it might be a proper name in Indonesia.

And, for those who claim that everything about Obama's past is "settled science", there's this example of what we're told not necessarily being the truth:

In the released documents Dunham listed both March 15, 1965, in Molokai, Hawaii, and March 5, 1964, in Maui, Hawaii, as the dates and places of her marriage.

Your job: find those who definitively state that she was married in 1965 and ask them to reconcile it with the above. For instance, Wikipedia currently states "[t]hey married March 15, 1965" and links to this.