There are actually no brown bears living in Florida. The only species of bear living in Florida is the Florida Black bear.
The chef Nathan Cole is caught by traces of human blood being found on his meat cleaver. This test was run a couple of weeks after the cleaver was used to cut up a woman's body. This would be impossible as all traces of human blood would have been washed away, as all professional chefs wash their knives daily and sometimes multiple times a day.