For a couple of decades now, students who had completed their first logic class and dabbled in a little bit of metatheory (perhaps soundness and completeness) were forced to avail themselves of Boolos and Jeffrey's (fourth edition with Burgess) "Computability and Logic." Unfortunately, the third edition presented much of the material in too brief a manner, resulting in a big jump from lower level logic to the material covered. The fourth edition is much longer, but no more easier to teach to talented undergraduates. More recently, Epstein's book on computability was an improvement in this regard, but its logical coverage was much less.
Smith's book should now be the canonical text. First, the discussion and proofs are astoundingly clear to students who haven't done much logic beyond their first class. Pick any topic from B & J and Smith, for example primitive recursiveness, the tie between p.r. axiomatizability and axiomatizability via Craig's theorem, etc. and the discussion and proofs in Smith will be clearer, more accessible, and more clearly tied to the other relevant concepts. Second, the coverage is exactly what is needed to understand both theorems and the most important consequences and extensions. Third, the way he ties the disparate topics together (for example the informal proofs through Chapter 5 and their rigorizaiton through Chapter 18) is just fantastic. This is really important for helping the reader develop a deeper understanding of things. If you just pile theorem upon theorem it's easy for the reader accept them as true without developing any logical insight and appreciation of the landscape.
I don't know if Cambridge would allow this, but in the next edition they should seriously think about adding exercise sections like B & J and Epstein. If they did, I think this book would eclipse the other two for classroom uses.
It's not just for students, either. A colleague and I were arguing about something and we picked up Smith's work rathern than either of Smullyan's to figure out a point relevant to the debate. I find that my grasp of the relevant proofs is much cleaer for reading Smith (my colleague is much, much better at logic than me, but with Smith's help I won the debate).
It is both extraordinary and a cause for celebration when someone can combine in a logic text this level of coverage, rigor, accessibility, and funness of read. I don't think there is a precedent actually. In short, Smith's work is a service to Lady Philosophy. Joe Bob says check it out.