So a single working person indicates what kind of food they like, and mom who cooks for a family of 6 adds a couple extra portions to what she makes that night and delivers it to a couple neighbors. That pays for her whole family. Chefs could post updates of what they're cooking that night, and people could "follow" their favorite chefs and pick from the meals available. Chefs build reputations, etc. It's like the ebay for food service.
It builds local community, creates opportunity for people to start their own micro-business, and it works really well in a recession -- people spend less eating out, and people who need money can make some.
The potential challenges are city/state laws around food inspection, that would all have to be investigated and figured out. There are lots of caterers and personal chefs, so I assume there's a way to navigate all of that.
In a depression, the game is changed to such an extent that you'd be hard pressed to predict what people would need. Instead, go outside and ask them. They'll be easy to spot: lying in the gutters, begging for change, an in line at the soup kitchens.
So we'll need software to manage food usage at those soup kitchens, track incoming supplies to the homeless shelters, and good disease management tools. In short, pretty similar to disaster management software!
Good enough answer? Yeah, I know I'm getting snarky in my old age :-)
As for "Make Me Dinner" I read recently about doing on one of the "frugal" blogs that Lifehacker quotes from a lot about doing something like that. I can't recall if there was a website for it.
When looking for the actual post, I didn't find it, but I did find another one that I thought might make a nice website, (and which I was going to look for next), along the same lines of your question: the Swapluck (instead of pot-luck) http://www.getrichslowly.org/blog/2009/04/04/start-a-swapluc...
Or perhaps the same for gardening?
A house trading site so that you can trade houses with someone where your and their job prospects are better?
A better roommate matching site than any one I've seen so far?
A kid-sitting exchange site?
A more-local Ebay (not like Craig's List), more like the Ebay of old?
Apprenticeships?