Thanks to the recent pointers to checkmytrip.com, I tried, well, checking my trip. It worked like a charm, showed both Mrs. JHunter's and my flights - with one exception. We have a confirmed first class booking, even paper tickets, yet the website shows business for the trans-Atlantic leg and coach for the intra-Europe flights.
Searching on FT gives one older reference that there may be issues with the BA-Amadeus link which just may cause this type of discrepancy. Can anyone confirm this? Or should I start looking for a place to plant my palm tree?