I've just done our ESTA applications. Both were accepted.
I really don't know what all the fuss is about - it is exactly the same as the green form we used to have to fill in when on a plane approaching the US. Except that now they charge for it, and will only return $4 out of the $14 (each) if application is refused. It's a money making exercise!!
I don't understand why anyone would pay anyone else to fill in this very simple form. It takes a tenth of the time compared with filling in the form to get a photo-ID driving license.
They didn't even want to know our home address, or our flight number, OR dates of travel and duration of stay. Just the carrier and first address in USA.