Update: check-in at the airport was completely routine, and nothing unusual was mentioned.
Oh, the seat that was supposedly assigned to me by a BA phone agent was not in my record.... The plane was less than half full though, so I still got a decent seat.

To answer the question about the itinerary, no, it was not particularly complicated. A standard one with three oneworld carriers, like dozens I've done before. BA had only one flight in it, and one pnr. Iberia had three pnrs, and AA one. I always make sure to get all the pnrs for my trips.