I saw this thing taking off on video once, and the exhaust looked like it was shooting straight down in a unique way. My Russian friend was all excited about it but with limited Russian I couldn't understand what was 'special' about Proton rocket compared to regular liquid-fueled rocket. Anyone have insight?

It was U.S.S.R.'s moon rocket

Wrong, they had entirely different rocket booster in drawing board for that.
This was originally intended as booster for heavy military payloads.

www.fas.org...

Here's info about launches and videos from those.
www.spaceflightnow.com...

Actually they got past the drawing board as at least two of the N-1 rockets blew up during the testing phase. One of them went up while still on the pad.