I have twice travelled to the US with a B2 visa, each time I have been unable to use the on line check in.I cannot use the self check in kiosks at the airport.Someone at the airport has to actually see the visa in my passport.

I contacted BA about this and they said that their computer system cannot handle anything other than an ESTA but they hoped it could in the future.
The biggest problem for me is(as a lowly blue, non status) I either have to wait until I am actually at the airport to select a seat or pay in advance for seat selection.
I did ask BA if they would waive the seat selection charge in these circumstances, you can guess their reply