I think that Mrs. Salmon's significance is that she is shown to be the supposed bedrock of the legal system. She is shown to be an impregnable witness. Essentially, she is perfect as a witness, and represents the very best of the legal system in terms of how eyewitness supported testimony should work. Greene describes her in such a manner:
She was the ideal witness, with her slight Scotch accent and her expression of honesty, care and kindness. The counsel for the Crown brought the story gently out. She spoke very firmly. There was no malice in her, and no sense of importance at standing there in the Central Criminal Court with a judge in scarlet hanging on her words and the reporters writing them down.
For the narrator, Mrs. Salmon is characterized to be the very best of witnesses. She does this as her civic duty. She is not looking out for her own selfish ends. She believes that her purpose here is to ensure that there is an open and transparent pursuit of justice. She is characterized to be the foundation upon which the justice system is built. If she cannot be recognized as a good and effective witness, everything in terms of eyewitness supported testimony would fall asunder. It is through Mrs. Salmon that one recognizes this particular set of proceedings as an almost foregone conclusion, more procedural than anything else. In this characterization, Greene is able to set up the eventual fall that sets the events of an "extraordinary day" in motion, demonstrating the lack of certainty in any human made construction.