Do please check that your library by now has a copy of the second edition of An Introduction of Gödel’s Theorems (it really is significantly better than the first edition, with a lot of changes throughout). Having put in the work to improve the book, I’d like you/your students to have the best version available!
I’ve just updated the corrections page for IGT2(thanks to Richard Baron for spotting a few more, fortunately minor, errors).
In updating those notes I’ve removed a few unnecessarily fancy asides — the material appears in a different guise in the newest set of exercises for the book (which will you will find here). Indeed my plan as I work through updating the GWT notes is, at the same time, to add exercises on the topics of revised episodes as I go along.