One way to take advantage of the enthusiasm of an audience present at a screening is to gather their email addresses right on the spot. Bring a clipboard (or several) loaded with signup sheets that you print beforehand. Gather whatever information you think is relevant, but an email address is probably the contact info that audience members will be most likely to hand over. At screenings of The Yes Men Fix the World at South by Southwest, the filmmakers did just that and left the festival with dozens if not hundreds of points of contact to poll later about their political activities, later screenings, and eventual DVD release.
Of course not every film inspires the same level of "give me more" interest as that of a pair of humorous activists with an axe to grind. In every well-attended screening, however, there will be a group of folks who want to know when the film comes out on DVD or how to recommend the film to a friend. Capitalize on that immediate interest by letting those people take action in the moment.
Be careful about adding such addresses to your mailing list service in bulk. Your provider may ask you to use the "invite" feature instead of simply adding the addresses to ensure that the recipients really do want the mail you intend to send. Stay within the bounds of their service guidelines, however, and the clipboard-to-email method is a great way of adding new members to your list.