Should GitHub repositories be included in a resume or statement of purpose?
I would definitely include the links in your resume. Even if they're not finished, as long as they have clear documentation and everything makes sense, go for it. Before including it, I would go through as thoroughly as you can and try to read it as a third party: what does this mean, what's its purpose, how could this be done differently? Even if you don't actually change anything, it would be good to have comments and notes throughout the code that are understandable to a third party, explaining things like those 'major bugs' you mentioned.

As for where, I have a section in my CV for personal projects: I would suggest you do the same. Alternatively, anywhere where you are describing relevant interests, you can casually drop the link in. However you decide to do it, I think it would be good to give links to specific projects with a little description of what it is and why it exists. The alternative is to just put a link to your GitHub account in your contact, like you said, but I feel that sometimes that can not be very helpful. Sure, it's there for them to look at, but if you can engage them with a description of a project you've worked on and then give them a direct link to the source code, I think that has more impact than them having to look for it themselves.