My business partner and I have both quit our day jobs and are now in the middle of starting a company to solve this exact problem; we launch in two weeks. I'd love to give more details, but we're trying to maintain a very low profile for the next 6-12 months...
People don't go to the internet for local stuff like what's posted on that bulletin board because there is no good site for it. Because there is no good site for it, people don't look for that type of info on the net and the problem perpetuates itself.
Newspapers, for example, had online classifieds before Craigslist, but craigslist made it easy and cheap (or free). I don't understand why local newspapers don't have free online classifieds. It would drive up page views, give your community a sense that your paper is relevant, and allow visitors to the site exposure to your content further enhancing the experience and so on.
Something needs to be done by newspapers to add value to their customers lives. This could be it. Lets hope someone tries.
I don't think most newspapers would ever do this, because almost all newspaper revenue comes from paid print advertisements. They're afraid of undercutting themselves. Whether that's a rational fear, I'm not sure.
What is really needed is a way to bridge between the current way of doing things and the online world. For example if you could take a snapshot of all the information on that kiosk in the park on a daily basis and use it to populate a website.
I don't think it's a matter of reliability: most aspects of the Internet infrastructure are perfectly reliable. I think it is mostly a question of social convention: most of the people posting these ads don't think of the Internet first, and most of the people who might be interested in the ads aren't scouting the Internet. Part of the reason for both of those factors is age: the Internet is not nearly as pervasive among older folks (or in communities outside the Bay Area, for that mater).
Another reason is that the Internet is global by default, not local (with a few notable exceptions, like Craigslist). At least right now, there just isn't that much to be gained by putting local notices on the Internet: there's an incremental advantage, but it's not the sort of obvious, game-changing advantage that drove the adoption desktop publishing, for instance. That might change as technology improves (for example, being able to show highly locale-specific ads to someone based on the location of their mobile device).
Perhaps my phrasing was somewhat unclear. What I meant is "when a network is something we're taking for granted and which is as uninteresting as the water supply" - and that's just in developed countries. As long as networks are even vaguely interesting to everyday people, there will always be a lot of reluctance in using them.