  We prove that the integral points are potentially Zariski dense in the
complement of a reduced effective singular anticanonical divisor in a smooth
del Pezzo surface, with the exception of $\mathbb{P}^2$ minus three concurrent
lines (for which potential density does not hold). This answers positively a
question raised by Hassett and Tschinkel and, combined with previous results,
completes the proof of the potential density of integral points for complements
of anticanonical divisors in smooth del Pezzo surfaces. We then classify the
complements which are simply connected and for these we prove that the set of
integral points is potentially not thin, as predicted by a conjecture of
Corvaja and Zannier.
