What is a consistent lens to look at an artist's body of work?

Just take note of things you particularly like or dislike, trends you see emerging, things that you notice are different or changing over the films, both visually and within the story. It’s all about what you notice, which is the point of film, I would say.

Interesting. A friend and I did a similar thing in college with Bob Dylan’s albums.

Ultimately, the meaning or value is up to you to determine. But some context is good – either a biography or info on the time the film was made.

I second PupnTaco’s contextual information! Be aware of dated references, especially in film.

I would try to find Allen’s specific influences in the films and focus on what he personally is trying to present to you as an audience.

Personally, I’d watch each film without interruption, taking notes. Then, I’d watch it again with your friend, each of you sharing your comments, stopping / replaying scenes as needed to aid in the discussion. If possible, I’d have two TVs, side by side, each with a DVD player, so that as you got into the body of films you could have side by side comparisons (when needed) of scenes.

Don’t take notes. I don’t think you could ever appreciate the fullness of Allen’s films if you were distracted by spelling out your thoughts as you watched. Watch each film without interruption, and then write down what you found memorable. If you need to, go back and check out the details – camerawork, lighting, dialog structure and narrative processes…

As suggested above, it will help if beforehand you had some cultural context of what was happening as Allen made each film. What were current events at the time? What was the public’s perception of the topics that Allen was dealing with? What was life like in the localities in which he filmed? With that bit of contextual framing, and an open mind to what Allen is saying, I think you’ll get the most out of his films. And with every film you’ll get to know him better and better, even as he evolved and matured.