What do the coral and paperweight represent?

The coral paperweight is something old belonging to a time before the revolution. Thus, it is a tangible connection to the past which Winston craves. It also comes to symbolize the little room in which Julia and Winston think is an oasis from Big Brother and the party, a little bubble that exists on its own. They of course are never on their own and when the thought police brutally invade their fantasy bubble, the paperweight is smashed to pieces: their world symbolically and literally crushed.