Coase comes up with a definition of the "firm" as an organization that defines employer and employee, master and servant which satisfies the "plain man's" definition of the firm. Coase explains that transaction cost optimization can account for the need of the firm.
The thesis is interesting and his discussion of other theories is rigorous and useful, but Coase's conclusion and logic is limited in many of the same ways as the theories he tries to tear down.
First of all, the idea that there is some kind of curve that can show when a firm is the right size, albeit the firm may be in several product areas is a bit linear. Also, he doesn't really discuss in depth some of the knowledge and competence that can be held in a firm and account for its fitness or value. Obviously silicon valley and virtual companies didn't exist in 1937 when he published the paper, but I think that the technological advances that caused the scalability and transaction cost performance that gave birth to the firm are now giving birth to virtual firms and communities that transcend the firm.
As a paper to set the definition of the firm and set a milestone, it was very interesting.
Feburary 16, 1999
In afterthought and particularly after talking to Iwamura-san, it appears that Coase does describe the firm as something beyond the market. Iwamura-san noted after my reference to Coase that Coase was not the first person to think of this. In any case, some people, like Iwamura-san will argue that everything is just an extension of the market.