It's a bit disputed. It matters from which point of view you argue in this point. If we take the Bailò in Constantinople as example, Venice had clearly the first permament diplomatic mission at the Byzantine court; but the Bailò was also the "mayor" of the venetian quarter. I think that's the diplomatic mission, which is mentioned. Traditionally, the first permanent diplomatic missions evolved in the first half of the 15th century in Italy, and is attributed to Milan, Florence and Venice; however, some historians say, that this system was based on the venetian system and was established, when Venice had to consult her ally Florence in their war against Milan. Because of that, they didn't remove their diplomat in Florence.