on my Canon 300HS, shooting in 'low-light mode' reduces the resolution from 12MP to 3MP.  what is the benefit of this?  are there any other benefits to reducing the resolution setting?

I am not familiar with that camera, but that reduction to 1/4 of the original it sounds like they are treating each block of 4 pixels as a single "super pixel".  A big advantage of this is that they can crank the ISO way, way up and still keep the noise levels low by comparing the values of the 4 pixels and eliminating any that appear to be noisy based on being too different than the other 3 pixels.