Hmmm, I'm no expert but let me give this a try. My information is bound to be full of holes so this should be educational for me too.
MPEG is encoded with three values, Y, U, and V. Y (luminance) covers the shades of gray, which will be the key factor for a black and white movie. The other two chrominance values will probably be zero all the time. There may be some kind of data compression advantages because they should be consecutive zeros. However, they are also sampled at a much smaller rate than the Y value is, so the maximum advantage would be less than 50% (4:2:2 compression). However, I'm not really sure how it sees the data for compression. If it is looking at the YUV streams separately, there should be the possibility of huge compression with those UV zero strings. But if the stream is looked at serially (as in Y data, U data, V data, Y data, U data, etc) then there isn't much chance for significant compression. Maybe someone can set me straight with the MPEG2 codec.
Now, I can't see that there would be any significant advantages to be gained on the motion and frame comparison side.
Mono and Stereo should have space savings based on the number of channels and the rate those channels are encoded at.