What new technologies would the defense use today to prove Tom Robinson's innocence in the crime he was falsely accused of?
It is not so much an issue of technology as of legality. Atticus adequately proved that Tom Robinson could not physically have attacked Mayella. The jury disregarded this evidence and convicted him because he was a black man who felt sorry for a white woman and kissed her. Even with more advanced technology, they still would have convicted Tom Robinson.
I'm with mike-crupp on this one. In the court scene of To Kill a Mockingbird, everyone in the room knew Tom Robinson could not have committed this crime--even some of the jurors who eventually convicted him. In the end, then, more evidence would not have changed the verdict. What undoubtedly would have helped was a jury comprised of both men and women. Mayella's plight would have resonated with them. This, along with the incontrovertible evidence, would have given Tom Robinson at least an even playing field from which to be judged.
I'd like to suggest that today Tom would likely have received a fairer trial due to changes in social and legal conditions, rather than technology.
Probably one of the first things Atticus would have done is to request a "change of venue": since the affair had attracted so much local attention, and so many people were acquainted with Tom and his alleged crime, the trial might have been moved to a place where it would not appear as important to the people -- especially the jurors.
On the whole, race relations are much better than they were at the time. Possibly Tom wouold not automatically have peen prejudged guilty just because of the color of his skin, or the social status that went with his color. And possibly the police would have investigated the scene more carefully. I say "possibly" because I don't know how things actually are where the story was set, but I'm optimistic.
The Courts are subject to much stricter rules now than they were then; if Tom had been convicted he would have much better chances during review. As I recall he did receive proper treatment in the courtroom: the judge was very fair and knew the popular attitudes that he would have to deal with.
My point is that technology is not the device that will guarantee justice in any trial for a grave crime, but rather good judgment, careful procedure, and wisdom and fairness in the courtroom.
All of the characters could be made to undergo a lie detector test and/or a behavioral analysis interview. These technologies and advancements in the study of human behavior are more fine tuned than in the past and may have helped in the investigation and the defence during this case. Certainly Tom would be shown to be telling the truth, and there is no way that Mayella or Bob would be deemed as telling the truth. Mayella in particular would probably implode undert the pressure of the exam itself, never mind the actual results.
DNA would also be considered from any contact between Mayella and Tom and Mayella and Bob. With this technology they would look for tissue under the finger nails as "defensive" evidence, and they could possibly find Bob's DNA there, not Tom's.
The most likely technology that could be used to prove Tom Robinson's innocence today would be DNA testing. There are at least a couple of ways that DNA could have helped him. However, it is not at all clear that modern techniques would have done him any good.
Tom's best chance would have been if Mayella would have been brought to a hospital right away and examined. A doctor could determine whether she had actually been raped. If she had, there could then be a test done on any body fluids present to see if they had come from Tom.
But in the circumstances, Mayella would not likely have gone to a hospital. Her father would have claimed rape a couple of days later when there would no longer have been physical signs of the alleged rape even if it had occurred. If he did that, Tom would not be helped by DNA testing.