How are legal principles different than America today compared to when Miller wrote "The Crucible"?
Part of what makes the current system of justice theoretically more advanced than the setting of Miller's work revolves around the rights of the accused that are embedded in the legal system. The reality of the defendant having a certain set of inalienable rights that cannot be vitiated represent bedrocks of the American system of jurisprudence. These elements are nonexistent in Salem because the mere accusation of being referred to as "a witch" created a setting where individuals had to defend their innocence. In the current theoretical notion of American justice, the prosecution has the burden of proof to prove the guilt of the innocence beyond a reasonable doubt. In attempting to achieve this goal, the prosecution must prove their case by meeting an evidential burden which consists of physical evidence, motive, opportunity, as well as eyewitness testimony. Except for the last item, which was more subjective and hearsay, the need to prove these elements were not present in the Salem notion of justice. For example, Abigail's testimony is never cross examined, evaluated, or assessed. Rather, the mere mention of "witchcraft" creates such a emotional contagion amongst the citizenry of Salem that her accusations are taken as truth, as opposed to a sample of evidence that must be examined and cross examined.
The main difference in our legal system today compared to then is the level of protections afforded defendants.
In today's legal system, there are much stricter rules about what is to be considered evidence than there was back then. For example, witnesses in the Salem trials were allowed to say what they thought, what they'd heard other people say, etc. Today, witnesses may generally only testify to what they know (of their own knowledge) to be true -- not what they guess, etc.
The defendants also had no right to have lawyers to help them defend themselves and had no right to have witnesses appear on their behalf.