The paperweight, the old man in the prole bar, St. Clement's Church
The paperweight and St. Clement’s Church have SYMBOL written all over them. These items are remnants of the past that, because of the Party’s control, no longer have any basis in "reality." By surrounding Oceanians with propaganda, party doctrine and contradictory "facts," the people of Oceania no longer have a past. Their memories aren’t even reliable because, after all, what would you think if you distinctly recall X, but X is nowhere to be found in dictionaries or historical documents. Even your friends give you are "are you crazy?" look when you ask them. Thus, in Oceania, it becomes impossible for people to question the Party’s authority. Not to mention that whole threat-of-torture thing.
Fortunately, some remnants of the past do remain, and the "useless" paperweight fascinates Winston. He buys it as an attempt to reconnect with the past. Same deal with the old man in the bar – yet another attempt to get in touch with history. The old picture of St. Clement’s Church hanging in the room? Singing the song with Julia? Again, more representations of the past.
Notice a blatant and rather non-subtle artistic device: when the Thought Police come to lead Winston and Julia away, the glass paperweight is shattered on the ground. Hmm! It’s almost as if Winston’s chances at recovering the past are shattered, too. Funny how that works out.