The arms of Falcarius are where the name came from, so we expect them to be pretty stunning. The large claws of the arm are just that; they are quite extraordinary in the world of an herbivorous dinosaur. Most herbivores either use size or speed to protect them from predators. Many have other forms of protection, such as safety in numbers, but the large claws of Falcarius would certainly have made formidable weapons for protection against predators. Additionally, the claws are situated much like those of a sloth, and as such, are fairly ideal for pulling branches to the animal rather than grabbing and grasping.
The teeth of Falcarius are rather peg-like. In some other animals, like Diplodocus, we find these sorts of teeth and they are mainly for sheering leaves off of the twigs and branches from which the dinosaur fed. Because of this it is also highly likely that Falcarius ate in a very similar manner. Use of the hand like that of a sloth, for pulling down branches, while the teeth strip the leaves from the plant. The teeth are not designed for crushing and chewing plant matter in a highly efficient manner. There are a few teeth that appear to be for crushing plant matter, but they are very few and more toward the posterior end of the mouth. This probably entails the use of a gizzard in the digestive system, though as yet we do not seem to have compelling evidence of this organ structure.