Would you be so kind as to expand slightly on what "information from all the pixels" means to us plebeians?

Well with regards to the post I answered, some have the idea that you locate certain features like eye corners, mouth corners, etc. and then do recognition based on the measurements between these feature locations.

One of the earlier successes of face recognition as described in Pentland and Moghaddam's paper was to use simple PCA on the images of faces normalized by eye position. This PCA would use all the pixels of a vector made from an image. Obviously there's been a lot of progress since then, but all pixels are getting used for information.

A couple years ago I worked on a product that added a feature to do, not exactly facial recognition, but "facial similarity" perhaps. Not any kind of bleeding-edge research but just a helpful little value-add. The approach we took was exactly the kind of geometrical measuring of nodes that I believe you are referring to. It worked okay.

Principal Component Analysis looks interesting, but I'm struggling to understand how 2D pixel data would be transformed into the appropriate covariance matrix. Any insight on the missing link you could offer?

I would look here: http://en.wikipedia.org/wiki/Eigenface

The technology has advanced far beyond that, but that was the start where automatic face recognition first became realistically possible.

Would bet state-of-the-art is doing face recognition with http://en.wikipedia.org/wiki/Convolutional_neural_network or similar.