errata - Real and Complex Analysis, 3rd Ed. by Walter Rudin

Theorem 3.3: In the proof, there is a small typographical error at the beginning. It should surely be $t = \int_\omega f d\mu$ not $t = f_\omega f d\mu$ [David Eger]

Theorem 4.11: Rudin's quick in part (b), using a single proof and guessing that you'll immediately see the symmetry here. [David Eger]

Theorem 14.8 (Riemann Mapping Theorem) Incorrect usage of Schwarz' Lemma. Revised Riemann Mapping Theorem (pdf) [Anke Pohl]