That would be great, but I would hope it could be turned off. I have plenty of code on GitHub that's clearly marked as just something I put up in a few hours for personal use only, where I don't care if there's vulnerabilities or exploits. The code was written in the true spirit of hacking, fast and dirty in order to solve an immediate need.
Sure, it could be on by default but easy to turn off if you wanted to.
Thinking about it again probably it'd be best as a per-repro flag that made a little button appear somewhere saying 'security', 'code police' or something similar, leading to more info. Obviously it'd take a bit of work and generate some false-positives, but I could see a system like this being really handy if they accepted open contributions for filters, even if it was opt-in it would probably still help a lot of people.
Re dirty hacks, I guess I wouldn't publish things like that to github, I'd keep them in a local or private repo, as they're not for sharing. If they are for sharing in spite of vulnerabilities, turning off a warning shouldn't be too much hardship for you, and it could actually help others looking at the code quickly tell it wasn't to be used in production as it would mark it as unsafe.
Lots of generic hosting providers can be used for it too, if you have a hosting account somewhere. As long as the server has git and you have SSH access, you can do this on the server side:
$ mkdir project_name.git; cd project_name.git; git init --bare
That's what I do (on Webfaction). Of course, then you don't get all the fancy issue tracking and all that from github, but it works if all you need is a few kb of storage for a remote. That also makes it easy to deploy PHP projects with a single post-receive hook, since it's all in the same box.