Valencia, where Mr. Calatrava was born, has a lot to regret now that Spain’s economic boom is over. The regional government, led by the center-right Popular Party, spent, for instance, about $180 million on a new airport that has not managed to attract any airlines. And some critics see Mr. Calatrava’s City of Arts and Sciences as another monument to the government’s extravagance, not his. Did Valencia really need an opera house, they ask?

But other critics scoff at Mr. Calatrava’s landscaped gardens beneath metal arches that become so hot no vines will entwine them. The roof of the performance hall leaks, they say. The opera was once flooded in a storm. Didn’t he know he was working in a riverbed?

One Valencia architect, Vicente Blasco, has taken Mr. Calatrava to task in a local newspaper for even trying to cover the steel sides of the opera house with a mosaic of broken white tiles. (That touch was Mr. Calatrava’s nod to another noted architect of Spain, Antoni Gaudí, who favored mosaics.) The flourish may have been a nice idea, Mr. Blasco said, but it was absurd. The buckling that is now occurring was predictable. On days with a rapid change in temperature, he wrote, the steel and tile contract and expand at different rates.

“Maybe someone sold him on some special adhesive, but I don’t see it,” Mr. Blasco said in an interview. “It is so basic. No one would expect that to work.”1

• 1. New York TImes, A Star Architect Leaves Some Clients Fuming, Published: September 24, 2013