The only issue is that the runway is very short (5500ft) and has a mountain on the north side.
The mountain on the north side forces pilots to both land from the south and take off to the south.
That together with the short runway causes flights to be canceled when tail winds are above 10 knots. When that happens (more often in winter or during summer storms), flights are diverted to Bologna, then passengers are bussed to Florence (or viceversa).
The other issue is that due to these runway length limitations flights are subject to weight restrictions and cannot take off full at MTOW (maximum take off weight). Flights that cannot be filled to capacity cause higher prices, and in fact flying to FLR is often more expensive.
Other than that, if the weather cooperates when you go, it’s a great airport to fly into. Quick and easy.
Just one word of warning. Due to the short runway, the pilot has to slam on the brakes immediately after touch down. Therefore place your hands on the seat in front of you or you might hit your nose against it. But don’t worry. In the last 35 years only one plane didn’t stop before the end of the runway. So the safety record is good. Airlines subject their pilots to extensive landing training in Florence before flying there. And Airbus has equipped the planes operating there with a special powerful braking gear that is aptly called “Florence Kit” (but don’t forget to hold on to the seat in front of you).