I did a very similar trip to Italy with my wife in Feb. 2013, hitting Venice, Florence, Rome and Sorrento (Naples, Amalfi Coast & Capri) over 17 days. The best thing about Italy this time of year is that in the most touristy places (Venice, Florence, Rome), the crowds are relatively small compared to the peak months. The worst part, aside from the obvious potential weather issues (it was in the 40's and rainy while we were in Venice, but 50's/60's and sunny all other points south), is the number of restaurants that were closed for the winter. This wasn't really an issue in Florence and Rome, but in Venice and Sorrento - and especially in the Amalfi Coast and Capri, this was definitely an issue. I recall Positano, Amalfi, and Capri in particular as feeling as though they were pretty much shut down for the winter, as almost all the restaurants and most of the shops (and I would assume, hotels too) were closed. We still had a wonderful day hiking around Capri, as the weather was gorgeous the day we were there, but there were no restaurants open save for a tourist trap or two with unmemorable, overpriced food. Not sure if the boats to the Blue Grotto were available that day, we didn't consider it due to lack of time (were just there for a day trip).
I'd also say that you're trying to pack too much into your schedule, given the amount of days you have. Based on what I said above, I'd recommend cutting out Sorrento altogether and hitting that on another trip during the warmer months, while spending more days in Venice, Florence/Tuscany and Rome. If you stretch your stay in Venice by another day or two, you'll hit the start of the Carnevale festival (begins Feb. 16), which would be a nice treat, plus you'll have more time to get lost in the bridges, canals, and alleyways, which is one of the best parts of being there. Plus, bear in mind that you'll be jet-lagged (assuming you're traveling from USA), so you don't want all your memories from Venice to be foggy. One day is also not enough to see Florence, you'll want 3 days there at a minimum, plus the day you had set aside for a Tuscany tour. Three days in Rome seems short as well but you can see a lot in that time if you're not dead set on hitting all the major tourist spots, plus you still can make a day trip to Naples (only 1 hr. via high-speed train) if your jones for Pizza Napoletana is too great.