  In this article we discuss some applications of the construction of the
Ap\'ery set of a good semigroup in $\mathbb{N}^d$ given in the previous paper
[Partition of the complement of good semigroup ideals and Ap\'ery sets,
Communications in Algebra, 49, No. 10, 4136-4158 (2021))]. In particular we
study: the duality of a symmetric and almost symmetric good semigroup, the
Ap\'ery set of non-local good semigroups and the Ap\'ery set of value
semigroups of plane curves.
