Has anyone found an error in an early version of Neukirch?

In the last edition of Neukirch, Chap. II, section 10:

For a field with a discrete valuation, let $v$ be the valuation, $\mathcal{O}$ the ring of integers, $m$ the maximal ideal, $U^{(0)}=\mathcal{O}^\times$ and $U^{(s)}=1+m^s$ (for $s\ge 1$) the groups of $s$-th units (appropriately subscripted).

Let $L/K$ be a finite Galois extension where $K$ has a discrete valuation that has a unique extension to a valuation of $L$. Let $G=\text{Gal}(L/K)$ be the Galois group and for $s\ge -1$ let

$G_s=\{\sigma\in G,v_L(\sigma a -a)\ge s+1 \mbox{ for all } a\in\mathcal{O}_L\}$

be the higher ramification sugroups. Then Proposition (10.2) claims that for all $s\ge 0$, the mapping

$G_s/G_{s+1}\to U_L^{(s)}/U_L^{(s+1)} \quad,\quad \sigma\mapsto \sigma\pi_L/\pi_L$

is an injective group homomorphism that does not depend on the choice of a uniformizer $\pi_L$ for $\mathcal{O}_L$.

In fact, the injectivity statement holds for example if $\pi_L$ generates $\mathcal{O}_L$ as an $\mathcal{O}_K$-algebra, or if the extension of residue fields is separable, but it fails in general. Here is a counterexample.

Consider the field of Laurent series $k=\mathbb{F}_p((t))$ in the variable $t$. Let $C$ be a Cohen ring for $k$; this is a complete discrete valuation ring of characteristic $0$ with uniformizer $p$ and residue field $k$, and it is unique up to (nonunique) isomorphism with these properties. It may be described concretely as the set of formal series $\sum_{n\in\mathbb{Z}} a_nt^n$ whose coefficients are $p$-adic integers that converge to $0$ when $n\to-\infty$. Consider $\mathcal{O}_L=\mathcal{O}_K:=C[\zeta]$ where $\zeta$ is a primitive $p$-th root of unity; this is a complete dvr with uniformizer $\zeta-1$. Finally let $L=K$ be the fraction field of $\mathcal{O}_K$. The Frobenius morphism of $k$ lifts to an endomorphism of $C$ that takes $t$ to $t^p$ and acts as the identity on coefficients. This in turn extends to a morphism $K\to L$ that makes $L$ a Galois extension of $K$ with group $\mathbb{Z}/p\mathbb{Z}$, generated by $\sigma(t)=\zeta t$. One has $G_0=G$, $G_1=\{1\}$ and the map $G=G_0/G_{1}\to U_L^{(0)}/U_L^{(1)}$ is trivial.

Bosch, Algebra (one of the best new textbooks in German) used to have this slip in his Witt vectors chapter:

The lemma states a congruence modulo $p$, and the proof begins by WLOG assuming that $p$ is invertible in the ground ring.

It was fixed in the 7th edition in a way I don't really like (the absurd sentence has been replaced by "we can assume WLOG that $p$ is not a zero-divisor in $R$", which is correct but not quite obvious at the point).

In my edition of Neukirch, Chapter I.9, Exercise 2:

If $L|K$ is a Galois extension of algebraic number fields, and $\mathfrak{P}$ a prime ideal which is unramified over $K$ (i.e. $\mathfrak{p} = \mathfrak{P} \cap K$ is unramified in $L$), then there is one and only one automorphism $\phi_{\mathfrak{P}} \in G(L|K)$ such that

$\phi_{\mathfrak{P}}a \simeq a^q \ mod \ \mathfrak{P}$ for all $a \in \mathcal{O}$,

where $q = [\kappa(\mathfrak{P}) : \kappa(\mathfrak{p})]$. It is called the Frobenius automorphism. The decomposition group $G_{\mathfrak{P}}$ is cyclic and $\phi_{\mathfrak{p}}$ is a generator of $G_{\mathfrak{P}}$.

Typo: That should be $q = |\kappa(\mathfrak{p})|.$