Corrections and additions to "A note on the hit problem for the polynomial algebra in the case of odd primes and its application'' [Rev. R. Acad. Cienc. Exactas F\'is. Nat. Ser. A Mat. 118 (2024), article 22]

In this work, we correct some erroneous results in the published paper [Rev. R. Acad. Cienc. Exactas F\'is. Nat. Ser. A Mat. 118 (2024), article 22]. In polynomial degree $p+1$, the kernel of the first reduced power has a basis of non-hit elements, disproving the asserted kernel--image implication. The published Frobenius construction induces the zero map on indecomposables, whereas the general multiplier fails even on the restricted hit expressions in its premise. We give a three-variable counterexample for every odd prime, prove a replacement with explicit degree hypotheses, and classify the monomial multipliers of Frobenius that preserve hits in one variable. For the third transfer, we correct the dimensions of the targets in the four principal degree families and establish surjectivity throughout those families. We also recover the independent surjectivity assertion in six further families. Explicit invariant-space calculations and Minami's degree reduction prove isomorphisms in six infinite families at $p=3$ and $p=5$, including a family in which the domain and codomain of the transfer are both two-dimensional. An appendix gives explicit representatives for every nonzero rank-two invariant line in the classical dimension classification.