The first huge fallacy is to engage in social media thinking that it's only a channel to communicate or sell to an audience that is often thought of as "captive". There is no such thing as a captive audience these days, firstly because people are free to allocate their attention where they want consciously or not, secondly because attention is scarce and thirdly because the platforms used by people are customising the content they show to them. As a result, no brand can think about an audience as being "captive".
A second big fallacy consists of believing that the audience will stay very disciplined and only use the content a brand provides for the purposes initially intended by the brand. That is not what experience teaches as people will use any point of presence of a brand to talk about any topic that they feel in important to them from rants about the service to enquiries about job offers or activism in favour of a cause like the environment or labor conditions with subcontractors (as the fashion industry is painfully learning). So no brand can consider its presence in social media as being just for one purpose and under the authority of just one silo within its walls. By the way, the current technological environment makes those very walls porous and therefore what happens inside ends up showing outside, often in a way that is neither pretty nor in line with the company's desires.
Last, but certainly not least, is the trend that has senior decision makers in many companies completely oblivious to the fact that heated discussions about tools and platforms will never replace rigorous thinking and decisions about strategy. A tool is a tool and has to serve a business purpose; the tool is not a master.
Here is an excellent article on Forbes about how social media will not fix a broken customer service. Very good food for thought for senior execs who need to learn more about the unique ability of the Internet and its technologies to break silos and compel all functions within a company to collaborate and converge to serve customers across all facets of the business on all customer touchpoints.