1984 is a highly symbolic novel, and symbols by their nature are open to multiple interpretations. Below are some examples of symbols and their interpretation, but the list is by no means exhaustive.
Winston's varicose ulcer is an expression of his consistently repressed humanity: repressed emotions, actions, sexuality, etc. His ulcer is introduced on the first page and begins itching terribly before he begins his journal. Orwell continues to refer to the ulcer throughout the work, and it gets better when he's living in a more natural, less repressed manner with Julia.
The paperweight is a concrete remnant of the past, and symbolizes the immutable past. The paperweight is shattered when Winston is arrested, which shows the control the Party exercises over the past.
In the room Winston rents there is a painting of a church. The painting hides the telescreen used to spy on Julia and Winston when they think they are alone. The painting is another symbol of the past, another concrete remnant. Because it hides a telescreen, this symbol could be read as an example of the Party being in control of the past.
The red-armed, singing woman represents to Wilson the hope that the "proles" can overcome the Party. Her singing demonstrates the individual, human spirit that remains undefeated within the "proles". Her tireless work hanging laundry shows the physical strength the working class possesses, a strength that could overthrow the Party.