I like the dialogue style of presentation. Reading a dialogue lets one see how a thinker actually thinks, rather than just reading works where all the rough edges have been sanded down. The main impression these dialogues made on me was not about Whitehead specifically, but rather that the salon is an excellent form of intelligent, civilized and civilizing interaction.
Price gives too detailed descriptions of the scenery on his trips to and from the Whiteheads. It would be better to have one or two lines setting the stage for the dialogues and a few lines between topics to give the reader a breather.
A complaint I have about these dialogues is that I was not familiar with many of the day to day subjects with which the dialogues deal, and I think that footnotes would be useful to orient the reader. For example, Dialogue IX starts with a discussion of some books about Boston that had appeared in 1936-1937.
An idea to which Whitehead returns is that we can't verbalize some important thoughts. "The real history does not get written, because it is not in people's brains but in their nerves and vitals." (p. 24) "Words do not express our deepest intuitions." (p. 238) He says that Bertrand Russell was a writer who composed in words directly, while he composed in concepts and then tried to find words into which those concepts can be translated (p. 149). I find Russell a much clearer writer than Whitehead. I agree with Whitehead that we have intuitions that we cannot express with words, but I think that hard work sorting out just what one means and rewriting (which Whitehead says in one of these dialogues that he doesn't do much) goes a long way.
Whitehead makes many statements in this books that are worth reading and thinking about. Let me give my favorite quote from this book. Talking about free will, Whitehead says "I think that although in the final act we are so conditioned by unconscious previous thought that it looks automatic, as a matter of fact we have been determining that act by an enormous amount of rejection and selection. It all depends on what ideas are entertained and how we entertain them; some may be dismissed at once as horrible and repugnant, others dwelt upon as pleasant. After this rejection and selection has gone on for a sufficiently long period, the final act is conditioned, but we have had a large share in doing it." (pp. 157-158)
There is a nice discussion on pp. 204-205 about developing the latent abilities of people. Also on p. 278 there is a brief discussion about adult education. On p. 264 Whitehead mentions that by continual expression rather than getting intellectually worn out, a thinker "brings vague ideas into precision by putting them into speech or writing; and by expression he develops his ideas and finds his ways to new ones."