I'll be traveling to Rome and Venice in late September; are there any physical gestures, meal customs, thanking policies, and so forth that I should be aware of?
Wikitravel.org has some ideas, which I've collected and grouped together below. It covers mainly respect, religion, clothing, and advice for women.
One of my guidebooks said "be sure to ask for the bill, they aren't going to bother you by bringing it over to you when they think you're done." Yet every time we asked for the bill it turned out it was already tucked under a saucer or plate that had been delivered to us. Coffee or dessert or whatever. So be alert to the possibility and look for tiny slips of paper (like a convenience store receipt) being delivered with your food.
First of all there are quite a few gestures you should master in order to understand Italians. Here is a nice picture of the most importants:
[A note about the first gesture "What? (Where) (Why)": if you do that with a angry face it means something like: "What the f*** do you want?". It's not particularly nice. So, in order to really mean "What?" try to rise your eyebrows emulating a surprised facial expression]
You have to understand that Italians use to think that these gestures are known in every single part of the World, no one doubt it, not even remotely and that means you are expected to be fluent in Italian gestures. Be prepared. Once I was visiting San Gimignano, and on the bus a Japanese couple was taking a crazy amount of pictures. An Italian man, very proud of his country, said something like "Bello, vero?" [It's nice, isn't it?]. He soon realized the Japanese couple didn't know Italian so he resorted to (what he tought was) the universal language: the "good" gesture in the picture above. For his great surprise they didn't seem to understand it either so he walked away very disappointed saying "Giapponesi..." (Japanese..).
Unlike the States you are not expected to tip the waiter/taxi drivers/wathever. You can obviously do that but it's not a must like it is in the USA. Doing it is much appreciated but it means you received a service way beyond your best expectations.
When you first meet someone a shake of hand is all you have to do. On the other side, if you start hanging out with friends more consistently you are expected to double kiss the cheeks. I would say that in the North a male only kiss women and shake hand with other men while the girls kiss other girls too. In the South everyone kiss everyone, so it's easier. Here, again, Italians are not aware of the fact that in other countries this isn't the standard so they will probably just go ahead and kiss you in the first place. Don't be scared, this usually doesn't mean they want "more" from you. If you know what I mean. Refusing this kiss would just make them think you are a little weird.
Driving isn't as crazy as most Americans tend to think. Don't expect to find a semaphore at every intersection and you will be good to go. Ah, here you can't EVER turn right while red (even tho you will see a lot of people doing it anyway).
Italians usually eat sweet foods for breakfast as opposed to savoy foods. They don't fry hashbrowns with a crazy amount of butter, they don't scramble eggs and cook bacon. They just have an espresso or a cappuccino with a croissant. Also, dinner is usually eaten a lot later than it is in the States. Don't go to a restaurant before 19:30 or 20. 20:30 is the most common hour (the bigger cities in Northern Italy usually have dinner a little earlier than this).
An unconventional, though accurate, way of learning Venetian and Italian customs from a North American point of view is to read Donna Leon novels featuring Commissario Guido Brunetti.
More than a simple entertainment, they provide an insightful picture of modern Venice.