Before examining the scientific evidence, there are serious problems with the proposition that humans are omnivores. These philosophical issues fall into 2 distinct camps. Both of these issues seem to make the topic unsuited to scientific discourse.
1) Lack of a testable propositionClaims that humans are biological omnivores are hampered by the lack of any clear set of rules (i.e. a testable hypothesis) for establishing what an omnivore is. Some authors describe an omnivore as an animal that is neither a herbivore nor a carnivore. However, a definition of what something is not, is not a classification, in this case omnivores are said to be "nonspecialists", able to eat either plant or animal matter. But these kinds of poorly constructed pseudo-definitions are weak, because under conditions of domestication where technology is applied to foods, even unequivableherbivores can consume processed animal remains.
2) Confusion of similarities and equivalencesFood processing technology can bypass adaptations, allowing animals to consume things they would naturally be incapable of aquiring or consuming. Indeed the use of technology in preparing foods would tend to indicate a lack of adaptation. Specifically, the applying of food processing technology, i.e. hunting with weapons or trapping, cutting, cooking and tenderizing, to render animal matter edible, seems to contradict the notion of humans being adapted to capturing and consuming animal matter. There is clearly a world of difference between wild animals which naturally procure and consume animal foods, and civilised humans who consume meat, which is technologically processed animal matter. Similar arguments can be made regarding other foods that humans must process using technology before consumption.
As has been demonstrated, while there is clearly a similarity in that both humans and non-human animals exist that eat practically anything edible, the behaviours are in fact not equivalents. Wild animals procure and consume their food by using innate biological systems, whereas humans obtain and consume a wide range of foods as a result of technology.
If we are forced to concede that humans can be called omnivores, even though this results from the use of technology, then we must also accept that humans can fairly be called birds as a result of using flying machines, and fish as a result of using underwater survival technology. Such positions are unacceptable, and if persued, only convince us that the claim that humans are omnivores, is not based on any form of natural equivalence, as proponents intend when they claim that humans are omnivores.