The trick would be to take some features from a bunch of existing websites and combine them in a new way. There have been some attempts to join together the features of Google Maps and Craigslist, such as housingmaps, but so far these are mostly just been proof-of-concept sites. What would be extremely useful is a site like Craigslist that allows you to place various sorts of notices and adverts indexed geographically and that can display the information as map overlays. If that's all it did, you would just have a bigger version of housingmaps, but you needn't stop there.
Folks should be able to register one or more physical locations, and be able to call up a "what's new" view of a selected area. The older items would be grayed-out or missing entirely, and the newer items would be on top. This should make it possible to tell at a glance if anything is going on in the area.
It would also be useful to have an API for use by software that wants to query the site. That way it would be possible to write a bit of code for a GPS-equipped cell-phone and let it inform the user of selected events in the area they are walking through. It could even go as far as the oft-predicted 'virtual coupon' that could be offered as an enticement to folks walking by a store.
There is also no need to restrict the system to pull only. Folks should be able to subscribe to different categories of local information and have new notices delivered by email. Thus, everyone in an area who was signed up could find out about a lost cat.
That brings up an interesting point though: the system will be of limited use unless most of the folks in any given area are signed up. To encourage just that, the site should provide a number of local community services and forums for discussion. The aim would be to have the system become the de facto place to go to find out about public events in the community, to talk about changes to local bylaws, or just to get to know your neighbors.
This might be done by making alliances with local town officials so that they have their own special announcement categories and official forums via free privileged accounts. They, in turn, would announce the site in the quarterly fliers and similar community information channels that they would already have in place.
Thus, it would need to become a digital agora, an online place for the whole community to come together to discuss subjects of mutual interest, if it is to succeed at its mission of freeing our lamp posts of the faded notices that accumulate year after year. In the end, it would not be a small project, but it would be one well worth doing.
Updated 2006-03-26: Check out Loki, for a company trying something similar to this idea.