In the proof of Theorem 1.5.7 (in which it is shown the the nuclei on a locale, when ordered by pointwise partial order, themselves form a locale) in the computation at the bottom of p.35, there is used an inequality
$$ j\Bigl( \bigl( j(b)\Rightarrow k(b)\bigr)\wedge b\Bigr) \Rightarrow k(b) ~~\leq~~ j(b)\Rightarrow k(b)$$
however since $j(bla\wedge b) \leq j(b)$ and $- \Rightarrow k(b)$ is contravariant, I don't think that that's true.
I'm not sure what to do to avoid using this.