Istanbul is a nice city, but watch out! The last time I was in Istanbul at the main airport, my dad sat down our camcorder bag for not more than 20 seconds and he turned around and it was gone. Inside he had not only our cameras and camcorder, but some birth certificates and Iranian passports. Lucky for us, we had our American Passports safely kept with my mother. The airport security and police officers spoke VERY VERY LITTLE English and the best they could usually do was "sign" language with us. Our American insurance company covered our losses, but the whole situation while it lasted was a big hassle. Needless to say, make sure you keep a good eye on your belongings, because there are some expert stealers in Istanbul just waiting for a small window of opportunity.
Be sure to keep your wallet someplace secure!! I was stupid and had my purse hanging over my shoulder in a dolmus. When I left the dolmus my wallet was missing from my purse thanks to the fellas sitting behind me. Lucky for me there wasn't anything in it other than my credit cards and ID- the situation could have been much worse (i.e. my passport could have been in it)
Funny thing is, I was having such a wonderful trip, that having my wallet stolen didn't even phase me!! It's just a hassle to have to cancel and have everything replaced.
When you are in the heavily-touristed area of the Blue Mosque, lock everything down and clutch anything exposed to sight, especially high-ticket items like videocameras. Professional thieves hang out here, and they well know what to do as well as who are the best targets, so don't be one! There are also lots of police in the area, and as the thieves know better than to risk getting caught, you would do well to keep an eye on where the 'good guys' hang out, too.
Remember, they ARE there, and they will NOT go home empty-handed tonight. Just don't let it be your stuff.