Dr. Brennan and Dr. Saroyan argue about the age of the deceased person. Dr. Brennan says she will obtain an accurate age by carbon-dating the bones. However, as every Anthropologist knows, carbon-dating isn't used to determine the age of living (or in this case, recently deceased) things, it's used to determine when a plant or animal died. Since carbon-dating relies on the decay of Carbon-14, and since as long as an organism is still alive it is constantly replacing the amount of carbon in its system, it isn't until the plant or animal dies and the carbon is no longer being regenerated, that the amount of Carbon-14 starts to decay. Once an organism has died, over time the amount of carbon-14 decreases as it decays. It is by measuring the amount of Carbon-14 left in the body of a animal or plant that a scientist can deduce when the plant or animal died.
The goof item below may give away important plot points.
The key evidence in the case involves truffle spores found in the clothing of the murderer. The problem is that unlike other fungi, truffles don't release their spores into the air. The whole reason that truffles have such a wonderful aroma is that that is their means of attracting animals to eat them. Their spores survive the trek through the animal's digestive system and then get deposited in their stool where they grow into a new colony, if the stool happens to be deposited in a suitable location. In other words, there would be no occasion for spores to be in the clothing of the murderer.