When did Jerusalem first get an eruv for carrying on Shabbos? I've heard that Rav Moshe Feinstein pointed out that it didn't have one in Talmudic times. So when did they get one?
Rav Moshe Feinstein could not have said that, since it contradicts explicit passages in the Talmud:
אמר רבי יוחנן ירושלים אילמלא דלתותיה ננעלות בלילה חייבין עליה משום רשות הרבים
Rabbi Yochanan says: If not for its doors being closed at night, one would transgress for carrying in a public domain in Jerusalem.
Once the doors were closed, Jerusalem had an "Eruv".
Sotah 41a, Rashi "Mikan V'Elach":
מכאן ואילך. לאחר שגמר כהן גדול לקרוא פרשה בברכותיה כל אחד מן הצבור מביא ספר תורה מביתו לעזרה דקסבר . אין עירוב והוצאה ליום הכפורים אי נמי ירושלים דלתותיה נעולות בלילה ומערבין את כולה
After the High Priest finished reading publicly from the Torah, each one would go home and bring his private Sefer Torah to the Temple. Either the Gemara holds that there is no prohibition to carry on Yom Kippour or else Jerusalem's doors were closed at night and they had an Eruv around all of it.
Bava Metzia 53b, Tosafot Dinfol Mechitzot - דנפול מחיצות
Tosafot quotes - and agrees with - the Gemara quoted in Eruvin, discussing how the slaughtering knives could have been carried to the Temple on Erev Pessach that was a Shabbat.