What kind of biases can an anthropologist have that would affect their work? Any bias at all is the answer. Anthropologists strive to achieve a holistic and objective viewpoint upon cultures. Any bias at all can warp, alter and change an anthropologist's entire view of a culture and or society.
What most biases come from an anthropologist is a tendency called ethnocentrism. Ethnocentrism is the idea of interpreting another culture, judging them, based upon the views and value system of the anthropologist's home culture. This is opposed to the preferred approach of an anthropologist, viewing a society objectively and describing it factually.
What anthropologists strive for and focus upon obtaining is the idea of cultural relativism. Cultural relativism is the practice of describing, defining and understanding a culture, it's customs and concepts but not judging them. Cultural relativism focuses upon judging a person or people based upon their own values and moral systems. In essence it is trying to see from another culture's point of view.
The idea of cultural relativism was influence and introduced in no small part by the school of thought known as postmodernism. Postmodernism denies the existence of true knowledge in the world, it states that knowledge is a human construct that we must deconstruct so we may understand. The postmodern movement examines the limits of science and tries to view everything as a whole greater than the sum of its parts. The reason this is important to anthropology is that it emphasizes multiple ways of seeing the world, not a single ultimately correct way.
When concerning bias and anthropologists it must be kept in mind that no anthropologist can escape all bias. There will be bias in all anthropologists, the goal of anthropology is to do what they can to suppress their own biases and view cultures as relative to each other. Not judging a culture based upon an inapplicable value/judgment system (One outside of it's own) is vital to anthropology, but some bias is to be expected and should be watched for.
Martinez, Christian K. 2010. "Bias and Ethnocentrism in Anthropology". Associated Content. Posted: January 26, 2010. Available online: http://www.associatedcontent.com/article/2632281/bias_and_ethnocentrism_in_anthropology.html