Apart from the examples (which, as in the case Putnam, are arguably the most important part of the paper), Clark and Chalmers make two sorts of arguments.
• The first is that the sense in which the mind isn't limited to the head in their examples is different from that in the examples of Putnam and Burge (and they have in mind the examples you’ve seen in Davidson). When thinking about this issue, in addition to Clark and Chalmers and what Davidson says about the examples (including his own), you might think about Brooks, his ideas that “the world is its own best model” and that “the world grounds the regress of meaning-giving” (both phrases are quoted on the reading guide for Brooks and probably best illustrated in his paper by various comments on p. 304). And think also about Dennett’s idea of being fastened to an environment (see pp. 332f).
• Probably the more interesting argument for our purposes, and the one Clark and Chalmers give the most attention to, is their defense of the claim that their examples are really cases of cognition that isn't entirely in the head. Here, pay special attention to the example of Otto in section 4 and the four features of this example listed towards the beginning of section 5.