I think it is worth noting that there are many distinct goals for public outreach activities concerning science. These include the following:
Show that science is fun, cool, and beautiful.
Teach about science, both with regard to how it is done and what we know from it.
Recruit students to study science, possibly at a particular institution.
Lobby for increased funding for science.
Enhance the public visibility of a specific institution (lab, university).
Defend scientific knowledge as reliable.
This is particularly true of areas which have become politicised (partisan) such as climate change, childhood vaccinations, and evolutionary biology, and for which there are significant enterprises promoting "denial", "skepticism", or "alternative" views.
First, given these distinct goals, I think one needs to design activities that are tailored to a specific goal. Previously, I have discussed the problem of doing demonstrations for school kids that actually teach something about science rather than being like a magic show.
Perhaps one can achieve more than one goal, but I think it is unlikely.
Second, what is interesting and of great concern is that the last goal is a relatively new one. There are now sizeable (and sometimes very vocal) sections of the community who think science cannot be trusted. This is well highlighted in a recent Op-Ed piece in the New York Times, A Scientist's March on Washington is a Bad Idea by Robert S. Young. I agree with his argument that given the nature of the problem a march may be counter-productive, particularly as it will be painted as just another "liberal" political lobby group. A better strategy is for scientists to engage with a diverse range of community groups at a more grass roots level. Sometimes this means using subtle and diplomatic strategies such as described in this NYT article and by Katharine Hayhoe.
Third, this problem is very challenging because it is part of a much larger political and social problem, particularly in the USA. There is now a significant fraction of the population who have become disenfranchised from and distrustful of a broad range of public institutions: government, multi-national companies, universities, mainstream media, Wall street, "elites", ..... and science gets lumped in with all that.
Postscript (April 25).
The Marches for Science have now happened around the world. There are broader concerns, beyond those raised by the NYT article, that are eloquently presented by Vinoth Ramachandra.