I have participated in and organized many such seminars. The advice above, especially Noah's, is very good. I will add one suggestion. In my experience, informal seminars in which the presenter has sole responsibility for studying and explaining the week's reading do not work. It's better if everyone in the group reads paper X or chapter Y, and prepares for themself a list of questions/comments/worked out examples of general statements/confusions, which can be raised during the seminar meeting itself.
My experience here is really based on graduate seminars aimed at reading a single textbook or paper; I'm not sure how well it applies to a seminar that, like yours, aims at treating a different paper each week. So I may be answering the question in the post title without actually answering your question.