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. They tend to rely on this seeming to be true with limited argument and don't consider much in the way of arguments from the other side, so there is probably not much to discuss (which is not to say that it's clear they are right).

Probably the more interesting argument for our purposes, and the one they 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.