Is there a good errata for Shafarevich's Basic Algebraic Geometry? I don't seem to be able to find one through google.
Springer printed an Errata supposedly to be included in a study edition of the text to be published in 1977. I purchased the original edition directly from Springer and they mailed me the Errata at a later date. I don't really know what transpired in the intervening years.
I don't know if it is included in the errata or not: on page 10, about the proof of the representation, he noted that the proof that there are only finitely many points for which $p(x_0,y_0)/q(x_0,y_0)$ equals the common roots of the denominator of $\phi(t)$ and $\psi(t)$ uses "similar reasons", as noted: "for which this fails, for similar reasons", referring to $q$ and $f$ being coprime. But I think this is due to that fact that the function $p/q$ would become constant on $k(X)$.