Current ESTA has been used on BA into Houston twice and Air New Zealand into LA.
The system logs point of departure from the US, though you don't have to volunteer that information and these have been on BA ex Houston and Virgin Atlantic ex Orlando.
I have not been back into the system to change destination or carrier and have had no problem. Nor have I changed my destination address but, of course have filled out an address on the customs form.
Talking to the officials the ESTA has the effect of the old multiple entry visa for the two years of its validity.
Next trip, I'll ask if the ESTA has to be in date for the duration of the stay.