According to this question, the "could not parse proxy url" bug was solved more than 2 years ago.

However, when using the client-side OAuth flow, the aforementioned error message appears when executing SE.authenticate. Moreover, neither of success and error functions within SE.authenticate are executed. Instead, the user will be redirected to a page that tells him:

Application Login Failure

An error occurred while login into an application.
Error Details

error description: could not parse proxy url

although the login is successful, as the username appears in the page top navbar.

I encountered this error while developing a Firefox add-on that uses Stack Exchange API. You can confirm the bug by visiting this SE documentation page and clicking on the demo "Run Example" button at the bottom of the page.