After you spy on Fango the first time, grab some bobby pins from Nancy's dresser. Prudence Rutherford calls you, and it's a conversation you can't skip. You only have one conversation option here, since it's early on the game. Avoid talking about it; end the conversation as soon as possible.
Go to Campo Santa Maria Formosa and get the tracking device. While you're here, get all the things you need for the Samantha Quick costume. Then go to Fango's and feed the tracking device to the pigeon. Hide when Fango arrives.
Go to Campo Santa Margherita and find your pigeon. You want to root through the garbage to get the letter about Samantha Quick. You have to use the Italian dictionary on it, or else you won't be able to buy the sunglasses from the kiosk. Get the sunglasses, then go to the Ca.
When you go to the Ca', you get the conversation where Margherita tells the others about the excuse Nancy gave earlier. You know, the one where Nancy can say she's spying on someone. I guess the two conversations aren't THAT far apart. I'll still have to replay the game three times, to determine how long they are.
At this point, it seems that the game gives you a few options. You can look at the microdot with the microscope, you can spy on Fango, or you can go forward with the Samantha Quick impersonation. If you look at the microdot and leave, Sophia will call you, and you get the long conversation about Il Dottore. I think you can put this off until later? I think you can also ignore spying on Fango, as that just tells us he resends a pigeon, if his first one doesn't get received.
I'm not sure which option is best. I'll try to figure it out tomorrow.