1) Bring really comfortable shoes. I thought I had but ended up buying sneakers on our second day in Istanbul. It's a city for walking, with hills and cobble-stoned streets.
2) Bring earplugs so the dawn call to prayer, broadcast over speakers from the mosques, doesn't wake you.
3) Buy an Akbil for public transportation; it provides multi-ride (you decide how much) access to trams, buses, the underground, and ferries.
4) Resist the impulse to respond with a polite "No thanks" or "I have enough carpets" to the incredibly numerous and aggressive touts in front of the carpet stores. That only encourages them; the only way to escape engaging with them is to avoid eye contact and to act as if you don't speak English.
5) If you take a taxi, make sure the driver turns the meter on as you head off.
6) Be very careful of the restaurants that cater to tourists, which rip you off while acting incredibly friendly. Common scams: Pouring bottled water after you sit down and then charging you for it. "Specials" presented by the waiter are often much more expensive than similar items on the printed menu. Ask the price of anything not on the menu and repeat it back to the waiter to confirm -- better yet, scribble it down to confirm (we were charged 48 TL for something we thought was "for 8 TL." Another time, when we said we'd share a dish, we were charged double, and told that the one plate we'd gotten had double the usual amount of food since we were sharing. (If you're going to share, don't announce it in advance.)