Hi Guy Betsy,
I've experienced several annoyances with LanChile, another "questionably great" oneworld partner. The worst occurred last month, as follows. (Sorry to those who have read this story already in the AA forum.)
I had a full-fare J ticket on American from México City to Buenos Aires, connecting in Miami (MEX-MIA-EZE). The MEX-MIA segment was badly delayed, so AA, after trying to put me on Aeroméxico and Méxicana, ended up issuing me a first class ticket on LanChile, connecting in Santiago. Long-story-short, LanChile refused to honor the ticket, and my only option was to fly in a middle coach seat in the back of the plane. I wasn't too happy, but I needed to get to Buenos Aires, so I took the middle seat. Ughh...
That was definitely the worst "one world" experience I encountered. LanChile's complete disregard for a ticket issued by AA on their airline proved to me that oneworld still has a long way to go. My confidence in oneworld was shattered by that experience.