The party slogan "Freedom is Slavery" is a good example of a contradictory perception. The citizens see themselves as free. They don't think of themselves as slaves (Winston might). But what they do not realize is that they are slaves to the Party's wishes. The end of the novel basically proves it. Winston is brainwashed into becoming an automaton that follows the party line verbatim.
I think another false perception in the novel is Doublespeak and Doublethink. The language is being pared down, and words are being eliminated from the language. It's perceived by people as a way of streamlining the language and allowing them to hold two thoughts (more thinking) in their head at the same time. The concept of Doublespeak is sold to the people as a way to be more efficient with language. The contrary is actually true. Eventually the people will have no words left to express negative Party thoughts. There will not be enough language to adequately express oneself. And if the population can't effectively express themselves, then there is no way to organize and fight against Party rule. The population is slowly being dumbed down in order to become more pliable to the Party.
For physical proof, I would use the photograph found of Rutherford, Jones, and Aaronson together at a certain time and place. It proves that the three men were NOT where the Party claims. Everybody assumed and perceives the Party's record to be accurate concerning those three men, but Winston knows (and could prove) otherwise.
Some other good examples of this might be when Winston's early perceptions are contradicted by his later experiences (Mr. Charrington and O'Brien both come to mind as examples).