p64. In 2.1(b), both maps should go from $E(a,b)$ to $E(a',b')$, not the other way --- if $(x:y:z)$ is a point on $E(a,b)$, then $(c^2x:c^3y:z)$ is a point on $E(c^4a,c^6b)$ (Samuel Mayer).
p82. In II, 4.2(b), $\bar{E}(\mathbb{Q}_p)$ should be $\bar{E}(\mathbb{F}_p)$ twice (Francesco Minnocci).
p256. In the case of elliptic curves, the theorem of Siegel was first proved by Mordell.