We are staying in Florence for 3 nights but 2 of the days will be all day tours out of Florence. However, we do want to travel around on the evening we arrive and the morning and early afternoon of our departure day and take in at least the Accedemia museum, possibly the Medici Paris, maybe the Uffizi and maybe Pitti Palace, maybe the top of Duomo Dome at night, etc. Would the card be worth it or should we just deal with the clunkiness of paying for public transport without the card?
Florence is easily walkable, so you will not be taking public transportation to get to the sights you list. So you should definitely not buy a Firenze Card just for transportation.
As to whether it's a good deal otherwise, you just have to add up the cost of what you're definitely seeing and see how it compares. Remember that you have allotted very limited time to Florence itself, so there's a limit to how much you can actually see. Therefore, it would be hard to make any pass pay off, and you'll probably do better with reservations at the Accademia and the Uffizi. Here's Rick's directions for how to get these: http://www.ricksteves.com/watch-read-listen/read/articles/making-museum-reservations-in-florence
Harold above is right on target. If seeing statue of David - get reservations and go right when it opens around 8 am. After 9 am, the flood gates open and it gets crowded fast. You really need to look at Florence attractions and times sites are open/ closed and pick out just a few for just one day. Here's an example - start with David at 8 am. At 9 or so be at either San Marco Monastery/church or go to Duomo complex just a short walk from David. See the Baptistry, Duomo, and do either the Dome climb or the Campanile ( bell tower) climb. Don't do both. (Check out how long the lines are and wait times first.) The Duomo museum is completely closed until 2015. Get lunch. Then, pick one - two more sites and prioritize. Examples: Uffizi with reservations or Pitti Palace or Santa Croce Church or Palazzo Vecchio. You could probably do both palazzo Vecchio and Santa Croce. You can also save dome climb or bell tower climb until later in day and have shorter lines, if any. Palazzo Vecchio, I believe, may make a good evening site. Again, check times.
We plan on staying over by the Pitti Palace this Fall for 3 days. I have read in this thread that Florence is compact and that public transportation is not needed. Is this still true for trips across the bridges to Pitti Palace area?
Yes. Pitti Palace is a short hike over Ponte Vecchio. Brancacci Chapel requires significantly more walking, but can still be reached by foot by able-bodied persons.