Here in Jerusalem, where of course there is an eruv, I often see men on erev Shabbat and Shabbat morning, carrying bags of gabage on the way to Beit Knesset, to throw out on the way in a municipal garbage bin. Is that a problem?

One is permitted to through out bags of garbage, especially if it has bad smell and is disturbing to those in the house. Obviously as you have stated, it needs to be inside the Eiruv. (Shmirat Shabat 82,45) Rabbi Baruch Kitay