  We give an example showing that the product and linearization formulas for
the Wick product versions of the $q$-Charlier polynomials in (Anshelevich 2004)
are incorrect. Next, we observe that the relation between monomials and several
families of Wick polynomials is governed by "incomplete" versions of familiar
posets. We compute M\"obius functions for these posets, and prove a general
poset product formula. These provide new proofs and new inversion and product
formulas for Wick product versions of Hermite, Chebyshev, Charlier, free
Charlier, and Laguerre polynomials. By different methods, we prove inversion
formulas for the Wick product versions of the free Meixner polynomials.
