In "1984" name two things that Julia believes are fallacies propagated by the party that have never occurred to Winston.
Julia, having been raised almost directly by the Party's influence over the years, and having gone to a lot of their schools and participated in their programs, has some deeper insights into the Party than Winston does. Winston has a feeling of hatred for the Party, yes, but at this point he isn't quite sure of all of the reasons behind what the Party does, and why he dislikes it so much.
One thing that Julia has more insight into is how the party tends to harness the powerful drive behind sex into energy and excitement for the Party and for war instead. Winston used to be so sad over his wife's reference to sex and children as their "duty to the Party," but Julia understand perfectly and says she was taught that very principle. She says it makes sense to her, and explains that
"sexual privation induced hysteria, which was desirable because it could be transformed into war fever and leader worship."
Julia understands that there is a lot of power in restricting sexual enjoyment on private terms, and channeling the resulting frustration into energy for their own causes.
Another thing that Winston had never thought of before that Julia believes is that the wars are not real. She believes that they are all made up, and fictional devices to keep the people enslaved, used to limited resources, and patriotic and loyal to the Party. Winston hadn't thought about that before. So, the idea that sex was an awful, horrible thing to be detested, and that the wars are real are two fallacies that the Party are preaching that Julia believes to be false. She helps to open Winston's eyes to potential holes in the Party's armor. I hope that helped; good luck!