  We report the result of our evaluation of the Feynman diagrams appearing in
the determination of the four-loop renormalization group functions in the
two-dimensional lattice O($n$) $\sigma$-model by Caracciolo and Pelissetto. In
the list of the integrals used for the determination of those functions, we
find that three entries were not correctly evaluated. We give the values for
them corrected by us including those for all other integrals which we computed
with higher precision. These results are then applied to revise the
determination of the second analytic correction to correlation length $\xi$ and
spin susceptibility $\chi$ by Caracciolo et al. as well as our determination of
the mass gap by means of a finite volume technique where we explicitly made use
of the four-loop $\beta$-function. In both cases we find sizeable changes in
predictions. In the meantime there appeared a paper by Alles et al. where they
revised one finite integral in the list of our corrected integrals. After
having taken the new revised value into consideration, we found that there are
no noticeable changes in the perturbative predictions of the present paper
including the final conclusions.
