Italy: Buy train tickets in advance?

Pro:
You save more money on have more option times on those routes the sooner you book and don't have worry about paying for them in case you lose your wallet as long as you got a PDF copy
Con:
You spend more money when you get to Italy on train tickets on those specific routes, the train at the time you want could sell out

Tickets tomorrow for Venice to Florence are 53 EUR, April 8 they can be bought nonrefundable for 26.50 EUR, half price.

So if you have a hotel booked in Venice, and a hotel booked in Florence afterward, you know you have to get from Venice to Florence on a certain day. Why not pick a convenient time and buy a ticket and save a little money.

Florence to CT can be done with regional trains that are always the same price and don't sell out.

CT to Rome can be done a couple of ways, but ticket prices and savings are similar to Venice to Florence.

Pro is the potential to save money and the Con is that the ticket essential is non-refundable, and non-changeable. For all trains except Regionale trains, you have three levels of fares -- Super Economy, Econ, and Base. The SE and Econ are discount tickets with restrictions and limited availability. Once sold out for that train, that day, that time there are no more tickets at that price. The Base fare is the walk up price that can be purchased anytime, exchanged, and refunded up till one hour after the train has left the station.

Jolene,

If you're willing to commit to a specific train, date and departure time for the Venice - Florence and Cinque Terre - Rome segments, you can save some money. As mentioned previously, Super Economy and Economy tickets have restrictions, so choose carefully before you buy those type of tickets. Regionale tickets are always the same price, regardless of whether they're purchased online, in advance or five minutes prior to departure. Note that locallly purchased Regionale tickets MUST be validated prior to boarding the train on the day of travel, or you'll risk hefty fines which will be collected on the spot. Online Regionale tickets do not have to be validated but have a "validity window" of four hours from the departure time stated on the ticket.

One other point to mention is that for the Venice - Florence segment, you can travel either on Trenitalia (Freccia) trains or on the competing Italo Treno. Use whichever one has the best price and best fits your schedule.

I normally use Trainline to buy rail tickets in Europe, as they sell tickets at the same price as the rail networks and sell tickets for a number of different rail networks (including both Trentalia and Italo). You'll need to specify the exact stations you'll be using in each city, using the Italian names (ie: Venezia Santa Lucia, Firenze Santa Maria Novella).