How can Winston be considered a heroic figure? What qualities does he possess that could define him as one?
Winston's heroism is initially reflected in little acts of defiance against the Party. Whether it's his clandestine relationship with Julia, the recording of seditious thoughts in his diary, or even the purchasing of the diary itself, Winston's petty acts of rebellion put him in a markedly different category from the hardcore Party loyalists. In a society in which heroism no longer has much meaning, Winston is undoubtedly a hero of sorts.
One of his most radically heroic acts is also the one that leads to his downfall: joining what he believes to be the counter-revolutionary Brotherhood. This particular act of defiance is somewhat different from the others. Here, Winston is doing something against the Party because he believes it to be intrinsically the right thing to do. He isn't just rebelling against the Party from within; he wants to destroy it from the outside.
I'd like to suggest, however, that Winston's most genuinely heroic act of all is his unwavering hatred of Big Brother. Even after all he's been through he still admits to hating him. Despite his willingness to betray Julia, despite his acceptance that "Freedom is Slavery" and that "2+2=5," he still retains that small spark of humanity, no matter how badly he's been broken, both mentally and physically. Of course, his heroic resistance cannot last forever; Room 101 will see to that. But Winston Smith's subsequent failure to withstand his fear of rats is an heroic failure, nonetheless. And in a society that's as brutal and as utterly soul-destroying as Oceania, that's probably about as much as we could hope for.
Winston Smith can only be considered a hero in a highly qualified sense. His mixture of the heroic and the mundane is indicated clearly by his name, which combines "Winston" from Winston Churchill (famed for refusing to accept defeat when fighting against seemingly invincible enemies) and "Smith," the most prosaic of surnames.
His heroic traits are his willingness to fight against impossible odds, risking his life in the process, and his stubborn quest to understand not only what was happening to him and society, but why it was happening. Although he tries to "get along" as best he can with the society he lives in, he holds himself apart from it at the same time, attempting to preserve his individuality. It would be ungenerous in the extreme not to concede his struggle some elements of the heroic.
However, he is a deeply flawed hero. To begin with, he is himself part of the apparatus of repression, being engaged in the rewriting of history. He goes too far in his desire to attack the Party, compromising himself morally when he promises O'Brien that he will harm children if he is ordered to by the resistance. He cannot separate his political struggle from his personal feelings, which lead him to become entangled with Julia, friendly with Mr. Carrington, and trusting in O'Brien, all of which decisions are fatal. His thought and actions are already infected by the Party, and since he is thus compromised, he cannot reach a fully heroic stature.