When I attempt to get the Amica fare from Venice San Lucia to Monterosso (Cinque Terre) Trenitalia website pops up a box that says "Offer cannot be sold with the type of place selected." What does this message mean?
It means that the Amica fare is not available for that route, probably because there is a regional train involved in your routing, where Amica fares aren't available. Either try for a route that doesn't involve a regional train, or try pricing Amica fares for the non-regional trains, then add in the cost of the regional fare (which should be about 10 Euro), then compare them to the overall standard fare. That does seem like quite a bit of hassle. ;)
Thanks, Norm. Yes, the route involved regional trains. I will try to do as you say.