This could lead to a situation where you, the site owner, are sued. This is probably why most people don't start a site like this.
Let's be generous and say:
Two mentions in the firehose would be sufficient for a correlation
8% of people twitter
25% of twitterers would tweet that they were food poisoned AND name the restaurant
25% of the patrons got food poisioning
Those are pretty generous numbers though, with the figure jumping quite significantly as they're tweaked. A 25% poisoning rate for a reasonably-sized restaurant would probably hit the news beyond Twitter anyway.
What happens when a restaurant subpoenas you for the personal details of someone who posted a derogatory report?
I find kmort's suggestion interesting - using Twitter (i.e., data that is already public) could be a smart move, as you would then be simply displaying the data rather than compiling/publishing it yourself - this could reduce your legal liability when (not if!) a restaurant wishes to defend themselves against a report.
A health scare can easily destroy a business like this so I'd be very very wary!