TL;DR version:
Can you authenticate with Facebook without having a callback URL for a web application since the web application isn't actually running on a server.
Full explanation:
I'm working on building a connectedTV platform application where the "app" itself is a bunch of HTML/JS/CSS running locally (like File -> Open on your desktop browser) and I'd like to integrate Facebook into this.
The problem is that all of Facebook's OAuth calls for the web require you to have a callback URL to redirect the user to in order to complete authentication. Here's the gotcha -- there is no URL for this application -- it's a locally running webpage on the device.
I know this is what out-of-band authentication was designed for, but I can't seem to find any documentation on how to use this (or how to do a non-callback OAuth flow) with the Facebook OAuth system.
You're describing desktop authentication or any situation where you are authenticating to FB without a server. The redirect URL you pass to the OAuth dialog is https://www.facebook.com/connect/login_success.html
When the browser redirects you can get the access token. You can read all about it in the FB documentation, way at the bottom in the Desktop Apps section (https://developers.facebook.com/docs/authentication/)
Just reread your question and since the application runs inside a browser you will need to open another window to authenticate and get the access token from that.