Perhaps I'm obtuse, but I can't see what the Holy Father has done wrong in Constantinople. In the Blue Mosque he bowed a silent head; what else would anyone do (though I'd like to know exactly what it was the Grand Mufti was saying, and it would have been jolly if the Pope had then taken the Mufti into a Catholic church and, kneeling with him before the Tabernacle, had said the Trinitarian Gloria Patri).
When he visited Hagia Sophia, the very neat things he wrote in the book there ... the Greek and then the Latin ... seem to me to make perfectly clear that he visited the place qua the consecrated Christian Church of the Most Holy Wisdom. An elegant and clever piece of contextualising and I would feel quite proud if I'd dreamed it up myself.
Then later, they say he asked Patriarch Bartholomew for a blessing; but all I saw was His All-Holiness instead* giving him a friendly kiss on the Zucchetto; and then attempting unsuccessfully to kiss his hand.
The Patriarch appeared to be wearing a cappa magna ... those wretched things get just everywhere, don't they?
*I suspect that not everybody in the Orient would necessarily approve of the Patriarch blessing the Pope ... some of those Athonite monks have strong views ... I wonder if Pope Francis thought of that side of things ...