Well if I remember right, the switchblade they brought in was the actual murder weapon. Fonda had just bought a similar one and had it on him. And I don't know what procedure would have been back then or even today for juries.
Having served on Texas juries, I know jurors are taken to lunch together and eat as a group and then return as a group to the courthouse, all under the watchful eyes of baliffs after being instructed by the judge not to talk about the case among themselves or with others. During voir dire and in instructions from the judge, jurors are told they cannot consider any "evidence" not presented in court. All of that means that Fonda could not have obtained the knife or presented it to other jurors in the jury room. The baseball fan could have made his game simply by reporting the improper action to the baliff who would have reported to the judge who would have declared a mistrial. That's how it would have worked in Texas. I'm sure the rules in your state are much the same.
As for Ed Beagley's prejudice, I don't think the movie (and it's been a long time since I've seen it as well) said he wasn't still racist, but I think it's realistic that even though a person might be racist, they're not going to allow an innocent person of that race to die. .
As for Cobb, yes he was angry, but he's never had a release for that anger until it was sparked with the jury. It was the first time that he brought that out in the open. I think the bit with Cobb is some of the best material in the entire film and the most realistic..
As I see it, however, his real anger with his own son has been redirected all through the film toward the young man on trial. Cobb is mad and he wants to see someone suffer as he has suffered. We learn only at the last that his son is the cause of his suffering and anger but we never learn why. More important, we don't know if that anger is resolved when he tears up the photo and bursts into tears. Does he realize that moment that he's been taking his anger out of a kid that he thought all along might be innocent? Is he crying because he realizes that despite his anger, he still loves his son? Does he change his vote because he believes the boy is innocent, or as a symbol of forgiveness for his own son, or out of frustration because he knows there will never be any relief or reconciliation? Or does it really matter why he changes his vote?
Despite what I see as a couple of flaws of fact and character motivation, it's still one hell of a story and a great performance by all. And like my wife keeps reminding me, "They aren't shooting a documentary!"