Using staging version of Joomla 3.3.7 - Also using MAMP on Mac. Also getting an error after GitHub credentials are entered:
An error has occured: 404

When using AMMPS on Windows, Joomla 3.3.7, getting this error when entering credentials:
An error has occurred.
0 SSL certificate problem: unable to get local issuer certificate

Issue only happens if you use your email as username. Use username, rather than email, and it works.

If you have special characters in your password, the error persists. This is the error I get when my password starts with 55@

An error has occurred.
0 Could not resolve host: 55@api.github.com

You cannot use the @ symbol in your password as everything after that is considered a URL.
HTH

I'm gonna close this as an external dependency. It's either a bug in the JGithub, JHttp, or JUri classes (or somewhere else in the CMS API perhaps).

I had a PR (joomla/joomla-cms#3387) once upon a time to fix this issue and I think it should still be fixed. It costs people a lot of time to figure out it is actually their password or username with the @ symbol that doesn't make Patchtester work.

The fix is in the how the authorization is passed as shown in this file:
https://github.com/joomla/joomla-cms/pull/3387/files#diff-e7bfabaeed9aaf4d928b3a1524107c50

I would like to ask to have another look or if you want me to do so, I can.

I think that PR just works around the root issue. Unless it really is specific to GitHub, you should be able to hit the same problem using any of the other social packages (JMediawiki is another one using a username/password authentication) and the same failure there tells me the problem is in a common dependency between the two. Now that I have my IDE open again, I'd say take a look into JUri (and now the Framework classes it extends) as both call $uri->setPass().