FYI: The areas not already pedestrian around the Duomo (basically the north side) changed to all pedestrian a couple of Sundays ago. This also changed a bunch of bus routes. I posted some maps up of the altered bus routes with details about the changes:
Florence Bus Map
Nothing is going through here - including taxis. It is great for the pedestrian traffic, but for locals it is actually a bit of a hassle as it cut down a lot of buses and left the Santa Croce side somewhat slighted (as usual!). It may also make your cab fare more since most taxis have a longer route around now. Also - Via della Spada is OPEN again to traffic off of Via Tornabuoni - don't get yourself run over there - I almost did last week!
Some pics of the new pedestrian area around the Duomo.