Winston is the only character whose point of view we have access to in the novel, a necessary precursor for the potential of an unreliable narrator. After all, without an external perspective, we can never be sure what he's not telling us, nor whether the context in which he presents the information is accurate.
Take, for example, the way he blames himself for his mother's fate. He tells Julia:
Do you know, that until this moment I believed I had murdered my mother?
Until this point, his mother has only appeared in hazy recollections and in bizarre dreams in which she (and his sister) are trapped in a pit while he is at the top.
Later in the story, it is implied that she was taken by the party because she refused to conform to their ideals. However, the lack of detail makes it difficult to be certain. It seems plausible that Winston may be hiding something, perhaps downplaying or omitting his own role in the eventual fate of his family.
You can apply a similar thought process to other characters. Syme, for example, seems to exhibit a level of intelligence that Winston enjoys but which he clearly perceives as a potential threat to the party. Syme later disappears, and we are given no further detail. Has Syme been taken by the party apparatus, or has Winston reported him? Did he, in fact, even exist, or is he an invention of Winston's terrified mind? Without external validation, we cannot be certain.
Likewise, we are asked to take at face value Winston's feeling that he is rare, perhaps even unique, in his free thinking. He regularly judges those around him as brainwashed partisans, unthinking victims of the party's propaganda. It never seems to occur to him that just as he is terrified of revealing his opinions and secrets, everyone else might be in the same position.
One could make a similar argument, perhaps, about any novel which is narrated by a single character and which contains any loose ends. Winston, however, has potential motivations to be unreliable. His conditioning under the totalitarian state will have primed him to keep secrets. The stress of his existence in such an awful world may have driven him mad.
The biggest reason we might suspect Winston's reliability, though, is made clear at the conclusion of the novel. - spoiler ...
Winston is brainwashed by the party and learns to love Big Brother
... meaning we can no longer be certain of the accuracy of anything he has said, in the entire novel.
