"The heresy of heresies was common sense... "
If both the past and the external world exist only in the mind, and if the mind itself is controllable - what when?... The party told you to reject the evidence of your eyes and ears. It was their final, most essential command." (pg 68) Why was the evidence about Jones, Aaronson and Rutherford important to Winston's reaching these conclusions?
It's in Chapter 7
What this means -- what Winston is concluding -- is that the Party needs people to believe whatever it says. It needs them and commands them to disregard what they know and to believe only what it tells them.
The case of the three men you mention shows this. It is clear from the picture he finds that the men did not commit the crimes that they confessed to. But this shows Winston how much reality has changed. He and others who have his job had changed reality so much that no one would ever take this picture seriously.
When Winston sees the picture, he realizes how the rewriting of history makes true memory and use of common sense very difficult in this society. People have to just rely on what the Party says.
Jones, Aaronson, and Rutherford are very important to Winston because he saw a glimpse of true reality in relation to them.
Working in the Ministry of Truth, Winston more often than not has to rewrite things the Party has said in the past. For this work, he usually requests reference materials that come to him through a system of pneumatic tubes. One day, the photo of Jones, Aaronson, and Rutherford comes across his desk seemingly by mistake and he realizes it is true evidence of reality outside what the Party depicts as reality. He throws the picture away down a memory hole but seeing it for a split second had changed him.
Winston's realization that the mind is a mutable thing able to be manipulated by the Party shows him that control of reality and thoughts are the Party's most effective tools. Common sense is heresy to the Party so the Party makes it impossible to practice common sense. No one can be entirely sure of anything because the mind can degrade and be fooled. As well, there is never any hard empirical proof of anything because the Party is always changing things so they are in line with the Party's current stance.
If anyone was able to produce hard proof of the Party doing one thing or another, it would inevitably lead to the collapse of the Party as Winston knows it. As Winston asserts in Chapter Seven:
Freedom is the freedom to say two plus two make four. If that is granted, all else follows.
Freedom relies on the ability of people to make sense of their world as it really is and anything less is to be enslaved and oppressed.
Therefore, the picture of Jones, Aaronson, and Rutherford showed Winston how invariably chained to the Party all its members are. The picture is what really made Winston aware of true reality and how the Party warps it as best they can.
Jones, Aaronson and Rutherford were three early Party leaders who confessed to selling state secrets to Eurasia. One day, during his routine work rewriting newspaper articles, Winston finds a piece of an old newspaper article that has accidentally gotten in among his papers. It shows that the three men were actually in New York City on a day they had confessed to being Eurasia selling secrets. To Winston, this is a concrete affirmation of his belief that there is an external reality apart from what the Party says is true. He ends by affirming in his journal that two plus two equal four, regardless of what the Party might assert.
Since Winston lives in a world of "facts" that can neither be proven nor disproven, this concrete token of reality matters greatly to him. He recognizes too, if dimly, why common sense is the greatest heresy. It can be used against the Party, to challenge their version of reality, and what the Party can't endure is to be challenged. As long as common sense exists as a form of power that can stand independent of them, the inner Party members feel threatened: their own power is not absolute. Further, since much of what they want people to believe is illogical and nonsensical, common sense is an especial threat. If people actually were to exercise and act on common sense, the whole Party edifice might collapse.