First the positive: This place is all about the location. It is right in the middle of things. You are almost next door to the Piazza della Signoria and the Uffizi Gallery, and about 3 min from the Duomo. Galleria dell'Accademia is at a 10 min easy walk.
The main issue with this apartment is the steep steps (and I really mean STEEP): if you carry heavy luggage, your physical fitness will be tested (specially if you just walked from the train station). Be aware of it and factor it in your decision.
Second issue, and this one might have been addressed by the host by the time you come, is the air conditioning units need maintenance or changing: they were hardly noticed in the August heat. There were a couple of electric fans that helped somewhat but what really saved the situation was the weather cooling down.
So, good location and if the owner addresses the maintenance items, can be a good (even great) place to stay for the right people.