We will be traveling from Rome to Orvieto, on to Siena then Cinque terre. From Cinque Terre to Florence and on to Venice. We're planning to purchase tickets for each town as we go, is this a mistake?
No. For a few short rides, point to point is cheaper in Italy. You might take a few minutes to search this site or simple scan back a few days to read the other responses to this very frequently asked question.
Jo, the routes that you describe will place mostly onto the slower Regionale trains. Rome to Orvieto is a Regionale or perhaps the occasional IC train. Surprisingly, the train from Orvieto to Siena will be a Regionale. Siena to the CT will most likely be multiple Regionales. Same with the CT to Florence although you may be on a slightly quicker Inter-City (IC) train. Florence to Venice will definitely be a high-speed.
If you have a really good schedule written down with dates and times, you can actually buy all of your tickets in Rome at the same time. If not, you can buy as you go along but it takes longer.
Note that you will receive one ticket for each train you are on and not one ticket for the entire run. Probably the only run you will have without multiple tickets is the Florence to Venice run.
Three last hints. Regionale tickets are the least expensive. Second, they don't have train run numbers or times on them. Once you buy them, they are good for about 60 days. They become valid for 6 hours once you stamp them in the little yellow machine in the train station. Third, they are good for any Regionale train making that run. You are not tied down to a specific date, train run or time.
The costs for Regionale train tickets are really inexpensive. Rome to Orvieto - 7.10E. Orvieto to Siena - 7.90E, Siena to Pisa - 10.80E, CT to Florence - 9.50E. The IC trains have a bit higher fare. A Eurorail type pass here is really a waste of money.
Italy is easy to compare. Since all that is really available is a saver pass at $188 for 3 days, this works out to about $63 a day or 50 Euro cost. (2nd class) Florence to Venice costs about 42 euro on the fast train(for which your would need to pay a reservation fee for with a pass), about 23 euro on the slow train, your Rome/Orvieto and Orvieto/Siena legs even cheaper.
Rarely does a pass pay in Italy, maybe if you were jumping from one end to another repeatedly, but then you should question your itinerary. Just plan on Point to point, second class is fine, Regional trains if you are on a budget are fine as well, a little slower, and more and more less frequent, but still available.
As others have said, a pass only pays when you are doing a very long leg. I bought a pass my first time in Europe but haven't since.
My travel style now is to keep my legs short so I don't eat up all my time in transit so a pass is never the better option for me.