Also see: https://forum.processing.org/topic/how-to-mirror-the-left-half-of-the-canvas

You can use the pixel array. To speed this up you can move as much calculations as possible into LUT's.
See: http://amnonp5.wordpress.com/2011/08/21/striate-cortex-advanced-pixel-manipulation/

A faster solution is to use texture coordinates on a single image.See the DynamicTexture2D example from this tutorial: http://www.creativeapplications.net/processing/geometry-textures-shaders-processing-tutorial/

Another fast solution is to use a fragment shader. In Processing 2.0 you can use the filter() method to apply a fragment shader to the whole window.

Thanks so much for the resources, I've seen your tutorials before but they look a little intimidating!! Where can I find details on the fragment shader? I'm not really seeing it anywhere in the documentation and it sounds like that's really what I need here.

Here: http://www.processing.org/tutorials/pshader/

Ohhhh my... INFORMATION OVERLOAD. I spent all day looking at all of those articles and the only thing I'm left with is- ugh.

I would seriously look into the texture thing, as you should be able to use a video as a texture.
After all, a video is just one image after another.
Instead of displaying those images, you can use it as a texture instead, and draw 8 triangles with it.
This shouldn't really run any slower than the video normally would...