Near the end of the section on the eiglah arufah, the Ramban makes an interesting comment. After noting that the performance of ceremony does not mean that the murderer is no longer to be hunted or found guilty if tried, he makes a small caveat. The murderer is to be tried and punished by the Sanhedrin, or the king.
Or the king? What does that mean?
It is well known that since the closing the Gemara there has been some evolution in halacha to deal with updated circumstances but much of this evolution has been in areas that affect the daily life of the Jew. Other areas, especially ones like financial or criminal law, have not been as thoroughly updated. This is not to say that the halacha hasn't tried to deal with modern issues. I recall reading about mutual funds al pi halacha years ago. But there is only so far the system can move without poskim taking huge risks with major changes.
Thus a woman is only to be declared officially pregnant after she has been period-free for three months. A positive bHCG and ultrasound do not factor into the mix. Then there is the issue of criminal testimony. According to halacha the only valid testimony is done by witnesses in the presence of the court. This obviously eliminates the use of video testimony or evidence provided by video or audio recordings.
Now proponents of pure halacha will note that no modern technology is foolproof, and they would be right. After all, in an era of Photoshop where movies like Forrest Gump rewrite history, is it so hard to consider that such evidence presented at a trial could be faked? Even in the 23rd century, this will still be a problem and almost cause Captain James T Kirk to be court martialed. From the obstetrical side of things, pregnancy tests can be wrong. I had an experience with one patient who bled during her first trimester and had an ultrasound that confirmed that she had miscarried. Two months later she came to see me to ask why, if she had lost the foetus, was she still gaining weight? A repeat ultrasound confirmed the presence of a health pregnancy! How many times has DNA analysis identified the wrong person in an important trial?
However, the limitations of technology do not prevent its use in the modern criminal justice system. There are checks and controls to decrease the risk of damage to the proceedings that forgeries can create. No system is perfect but the attempt is made. Unfortunately in the absence of a binding central authority today as well as the concern with absolute perfection in testimony, the halacha cannot accomodate to these changes yet.
But if one considers how strict the rules of testimony are as detailed in Mas. Sanhedrin, one quickly gets the idea that while the Sanhedrin may have done a boffo job of administering the legal aspect of Jewish culture during Temple times, it probably never managed to convict anyone. Yet it is patently obvious that a society in which the courts never manage to punish criminals is one that will quickly devolve into anarchy and we know that our ancestors had a functioning society. How did they manage?
The answer is in the brief comment of the Ramban. Yes, there was a Sanhedrin in Israel but, as detailed in a shiur by Rav Benjy Hecht from Nishma, there was also a parellel justice system run by the civil authorities.
This makes intrinsic sense as well. Halacha may have lots to say about lots of things but where traffic lights go and the standards for manhole covers don't seem to get much coverage. A parallel civil system would probably handle the great majority of issues like this, including keeping a functional justice system with more practical rules running. If the Sanhedrin couldn't convict the murderer - and based on what we know, they'd do everything they could to not convict him - it would be up to the king and his system to enforce the law.
This therefore is the answer to how a halachic state would have to work in this day and age. While rabbinic law would be enough for many areas of life, in others practicality and modern realities would have to take control. Yet this is not an admission of the inability of halacha to deal with issues since we see that even in ancient times, this method was part of the functioning of a Torah state.