Basically we are social animals, learn from our community and construct our knowledge base that way. However, social constructivism theory is in a mess, and needs to be cleaned up. You can start your reading here: http://en.wikipedia.org/wiki/Social_constructivism#Social_constructivism_and_education
Your question could be stated a bit more clearly. Disadvantage of using the theory? For what purpose? For instance, you could ask what are the current disadvantages of taking a social constructivist lens in the generation of guidelines for teachers wanting to implement discovery learning in their classrooms? What exactly are you aiming for?
as long as you use a social constructivist frame work in order to research and interpret communicative phenomena in general, I can see no possible disadvantages. The meaning of communicative behavior can only be constructed (interpreted) and never be explained in the sense of causal relations. A little bit more difficult is the question to which aspects of human behavior social constructivism can or should be applied. With voluntary, symbolic behavior like gestures or language usage this seems to be obvious (G.H. Mead). To which extent thinking and even perception is already social (Husserl) maybe questionable.
Whenever discussing theories/paradigms/worldviews in classes, I always told the students that none of the perspectives were "right" or "wrong," which was often what they wanted me to tell them. I told them to imagine that each perspective is like a pair of goggles - so, if you put on "constructivist goggles," there will be some things that you will be able to see that you could not through a different pair of goggles - but, you are also blinded to some things because of the goggles you are wearing. That is why I believe it is important to have more than one pair of goggles up your sleeves, but that requires a tolerance for ambiguity, which in my experience, many students do not have.
I recently wrote a paper published in The Clearing House: A Journal of Methods that explored some problems with contructivism as pedagogical practice focusing on "activity". However, within, I address a few major problems of social constructivism for learning:
1) Because schema are formed by building knowledge on prior knowledge, if we seek to promote a "social constructivist" environment we almost necessarily must abandon the idea that actual truth exists. This is a major problem because to endorse pure relativism is utterly in vain. Hard relativism is internally contradictory and, thus, necessarily false.
However, if we endorse a "social constructivist" classroom where the group determines what is true, we adhere to this fallacious view. I would argue that this is among the most pressing problems of such an approach.
Here is a link to the article I mentioned if you'd like to read the whole thing (you'll probably need to log in through your campus library to get access)
LINK 1: https://www.researchgate.net/publication/304662570_Student-centered_Education_and_Constructivism_Challenges_Concerns_and_Clarity_for_Teachers
LINK 2: http://eric.ed.gov/?q=constructivism+learning+theory&ff1=subTeaching+Methods&id=EJ1106715
Article Student-centered Education and Constructivism: Challenges, C...
The theory could force students to be dependent on others and limit their ability to think independently. second, understanding truth from the socio-cultural fperspective may cover truth or reality and its objectivity.