Is running an open WiFi network and allowing anyone to connect to it anonymously really that big of a problem? After all, it’s a very neighborly thing to do, share your connection with others who might need it. But of course, there’s the danger that someone will do illegal things (e.g. traffic in child pornography, download copyrighted materials, etc.) that will be directly attributed to you. At the very least, there’s the danger that they’ll misuse your bandwidth, and create so much traffic that your ISP takes notice and slows you down.
For an interesting read on the topic, this forum has many interesting opinions.
Bottom line: yeah, it’s a really bad idea.