The Privy Council has considered this in The State v Boyce (Trinidad and Tobago)  UKPC 1 (17 January 2006). The judgment notes different usages of the term "due process": there is a broad sense, (para 13):
"In this sense, the concept of due process incorporates observance of all the mandatory requirements of criminal procedure, whatever they may be."
And there is a narrow, constitutional, sense (para 14):
"… those fundamental principles which are necessary for a fair system of justice."
The absolute prohibition at common law of a challenge to the finality of an acquittal was not, the Judicial Committee held, part of the narrower meaning of due process (para 15). This conclusion required classifying the finality of an acquittal as a "broad principle":
"…the broad principle that a person who has been finally convicted or acquitted in proceedings which have run their course should not be liable to be tried again for the same offence is a fundamental principle of fairness. It is recognised as such in many constitutions (see, for example, section 20(8) of the Constitution of Jamaica) and in international human rights instruments: see for example article 14.7 of the UN International Covenant on Civil and Political Rights and article 4 of Protocol No 7 to the European Convention for the Protection of Human Rights and Fundamental Freedoms. But [their Lordships] do not think that the principle is entirely without exceptions (see, for example, article 4.2 of Protocol No 7) and they certainly do not think that it is infringed by the prosecution having the right to appeal against an acquittal. The possibility of such an appeal is accommodated in the qualification of the principle ("save upon the order of a superior court made in the course of appeal proceedings relating to the conviction or acquittal") in all the Caribbean constitutions to which their Lordships were referred (Jamaica, Barbados, The Bahamas, Grenada, Dominica, Saint Lucia, Saint Vincent and the Grenadines, Guyana, Antigua and Barbuda, Belize, Anguilla, St Christopher and Nevis, Turks and Caicos Islands, Monserrat) as well as the international instruments which their Lordships have mentioned."
Thus, the proceedings may not have "run their course" until any right that the prosecution may have to appeal against an acquittal has been exercised. Once it has, the broad principle of finality would apply.
It is sensible, of course, to permit an appellate court to correct errors that have occurred in the application of the law during a trial, whichever side they may have favoured. This point was made in para 16:
"…There is nothing particularly unfair or unjust about a statutory rule which enables an appellate court to correct an error of law by which an accused person was wrongly discharged or acquitted and order that the question of his guilt or innocence be properly determined according to law. Such a rule exists in many countries. It is true that in Davern v Messel (1984) 155 CLR 21 the High Court of Australia said that the common law rule was so ancient and well settled that a statute giving a right of appeal in general terms against the decisions of a court would not be construed as allowing the prosecution to appeal against a decision in favour of an accused person. Express language was needed. But the court did not suggest that the absence of a right of appeal formed part of fundamental due process and in the present case the language of section 65E [of the Supreme Court of Judicature Act] is clear enough."
Other interesting points made in this case are:
- Proceedings on indictment start with the filing of an indictment; where an information is laid indictably, that is just a preliminary to indictable proceedings but does not form part of them (para 22).
- An "error of law" can arise wherever the judge had made a wrong determination, regardless of whether it concerns pure law, or a mixture of fact and law. It thus can include rulings on admissibility of evidence and on whether there is a case to answer (para 24).
- In deciding whether a witness qualifies as an expert, it is wrong (and this was one of the errors made by the judge in this case) to focus only on the witness’s paper qualifications. The judge was also wrong to call another witness solely to comment on whether another witness should qualify as an expert (para 25, 26).
- Where an error of law has occurred, and an acquittal has resulted, the question whether a new trial should be ordered can depend on whether a fair trial is still possible. Here, the error of law was corrected (ie the provision creating the right to challenge an acquittal was held to be constitutional), but the appeal was dismissed because it could not be said that a new trial would be fair, 9 years having elapsed since the events in question (para 26, 27).