We had a nervous 20 minutes at US immigration yesterday while they decided whether to send us back to the UK as Potentially Suspect People.
Although we had our passports and ESTAs in place and in date and had been into the USA last year on them, a new regulation has been in place since Jan 2016. This states that anyone who has been to Iran in the last 5 years has to have a personal visa issued in their country of origin and their ESTA is not valid, even if legitimately applied for and approved.
Our immigration officer found an Iranian visa in my wife's passport (we had been there on a sightseeing trip) and invoked higher powers. Fortunately our trip was in 2009 so eventually they decided we were OK. But if we had been there after Mar 2011 we would have been on the first plane back home!
No warning from BA or any other source....