Is my Florida landlord liable for injuries sustained on his/her property?

The answer to this question really depends on where you fell. For example, if you fell in a common area like the hallway or stairs, and the hallway or stairs were not properly maintained, then you may have a claim against the landlord for their failure to maintain those areas. If, however, you fell on a rug in your own apartment, and you're the one that put the rug there, and the rug was bunched up, and it's really your own fault, then maybe under those circumstances you don't have a claim against your landlord.