Why do some minifigs have grey hands and some yellow? I have a lot of LEGO Sets and have noticed that some of them have yellow hands and some have a dark grey colour hands. Is this because some are of old design and some are of new design? Most old ones have yellow hands, though?

This minifig has yellow hands:



And this one has grey:
Hand colors other than yellow are generally used to either match skin tone in licensed themes, or to represent some sort of gloves. The police officer you mentioned is probably "wearing" some sort of motorcycle or driving glove:



When minifigs were first introduced in the late 70s, the only ones to have non-yellow hands were the space minifigs: