First the Conservapedia description of Coase is way off base, then Megan McArdle gets it wrong and uses "preference maximization" as a synonym for utility maximization.
Like any theoretical economic lens, Coase provides a way to look at allocations of resources through a simplified model. We learn a lot by discovering where the real world differs from the model, and the model helps us understand what we are supposed to be looking for.
The example MEgan McArdle gives in her post is actually the textbook example of the Coase Theorem, so it's pretty easy to show the problem with her description. McArdle seems to suggest that transaction costs are minimized because the homes are next to each other. Geographic proximity does not enter into the calculation of transaction costs, however. What McArdle misses with her claim of preference maximization is the initial distribution of property rights. It is clearly defined rights that will limit transaction costs and facilitate bargaining. In this case, the right to play music loudly and the right to peace and quiet are poorly defined. This prevents an efficient bargain. If the initial rights were clear, then the two parties could bargain to the point that either the neighbor who likes quiet pays the other to not play his music as loudly as he has rights to, or vise versa. At some point both parties will be satisfied and the outcome will be efficient.
Of course, the issue with using Coase is that is nearly all situations the initial rights are not clear, wealth effects skew bargaining positions and transaction costs are present. So in this case we would use Coase to explore what rights and costs exist that prevent an efficient solution.