Not very powerful compared with a lot of Nation States. It's main use seems to be to embarrass nations into going along with majority decisions, but even that doesn't work very effectively. For example, Japan's persistence in catching (and eating) whales for 'scientific' research. It would seem that the Green Peace vessels carry more clout in this area.
The USA, Soviet Russia, China - all the bigger and more powerful countries just carry on their own merry way. They don't seem to give a damn what the remainder of the world thinks. The UNO is an attempt at democratic world rule but there is so much shenanigans going on that it'll be a long time before anyone in power-politics takes it seriously.