Which of these qualities does the creature possess? What qualities does he not have?
This is a question with which philosophers and scientists alike have struggled for centuries. To take a purely scientific point of view, we are human due to our DNA makeup, our chromosomes. In that point, I would have to assume that the monster possesses human DNA, since he is constructed of human parts. But, of course, a body does not necessarily make a human, so let's turn to more subjective evidence.
Some say it is spoken language with makes us human. While animals have the ability to communicate, no creatures on Earth have such a highly evolved form of oral communication. Considering just the thousands of languages spoken on the planet right now is staggering. In this instance, the monster is human. Despite more modern depictions of a lumbering, grunting beast, the monster in the novel is quite articulate and well-spoken. When he encounters people, it is his appearance, not his lack of communication that sends them screaming.
Some would argue that our capacity for rational thought makes us human. Again, while chimpanzees, dolphins, etc. are highly intelligent creatures, no animal has ever created societies as complex as humans. We can think through problems and choose the best course of action. The creature thinks rationally as well, at least in some cases. He understands the concepts of justice, natural rights, alienation, etc. He is able to convince Victor to create a companion through rhetoric. However, he is also a cold-blooded killer. He murders innocent women and children as casually as we might swat a fly. So his rationality does fail at times.
There are so many other points we can consider. Is it our emotions, our passions that bring us humanity? The creature certainly possesses those. Some may further argue that our immortal soul makes us human, but since there is absolutely no way to prove that, or prove that creature does/does not possess one, I'll leave that be. In conclusion, there are many ways people think of human beings. All of them are important for the total picture.