Went over the Mongoose Traveller agents MoJ entry, and it is largely as many of you define it, crimes committed as Imperial High crimes as noted including extraterritorial starports and presumably space.
Notable features-
* MoJ handles everything- investigation, creating and assigning judges, prisoner transport and handling, prison operations. About the only thing they don't handle is the accused's defense.
* No jury trials, no appeal, verdict is final and binding throughout Imperial Space.
* In high profile cases the MoJ may assign a tribunal rather then a single judge.
* The MoJ IS sensitive to the function of appearing to dispense certain but fair justice as an element of ruling the Imperium.
* Judges come from the nobility.
* Resources are stretched so the MoJ makes use of hiring local LE, bounty hunters, professional security etc.
* The same resource issues means your supervisor may be 10 parsecs away, so Imperial agents have a lot of leeway to get away with unsupervised activity- this may allow corruption and abuse of power to occur, but penalties are harsh for being caught at it.
Seems very Napoleonic Law to me.
It's missing trial by combat (Duels), Guilty until proven innocent, Right to Counsel, and the jury trials of the Code Napoleon. (Note that Juries to bring indictments were not, but at least for courts-petite the Trial Jury was a presumption; the criminal judge alone issued indictments, IIRC. Other forms of trial could be agreed upon, including duels in maters civil.)
Note also that, if your list is accurate, then there's contradiction with prior sources, namely JTAS 14...
Violations of subsector and Imperial law are tried by a tribunal composed of from three to nine judges. (JTAS 14, p 22)
And MGT Bk2 (M)HG which mentions a Naval Command Grand Jury. (p 36)