My favorite dithering algorithm for motion video is Yliluoma dithering: https://bisqwit.iki.fi/story/howto/dither/jy/

It is especially useful for grayscale content, as finding the optimal dithering matrix from the available palette is a straightforward exact operation, and the result can be placed in a LUT for real-time rendering.

In my opinion it looks much better than bayer or random dithering, especially on gradients.