Accepted terms for summary execution:
Gila Munja: Gila Munja are to be terminated on sight when and if found within the confines of Mega-City One. Noted in the strip on several occasions.
Judge Murder: Summary execution noted several times in the strip.
Treason: Summary execution
Colaberation with an enemy that endangers Mega-City One, its people, etc, Summary execution. See Apocalypse War for more details.
Looting: several times looters have been shot dead for stealing during Necropolis, Robot Wars (2nd) and the Apocalypse War.
1st Degree Murder. Judges are empowered to execute perps who commit wanton acts of murder with no show of remorse.
Infection: Victims of diseases such as Wasting Bobos and Grubbs are often executed/euthanised to both end their suffering and stop any further contagion.
The exact details of summary execution have never been fully noted in either the strips or any of the Mongoose Publishing books, but the above are all documented. As noted above by Robin, judges who show excessive force can face a repremand for faliure to follow procedures. Good tip is to try and remind players that they are there to uphold the law and not to adminster their own brand of it. Also one last thing, if a citizen or perp shoots at a judge with intent to kill, maim or injure then they forego all their rights and if they are killed in return the judge will face no repremands.
I did have an article about full penal codes of statue on my laptop but it was stolen (the laptop that is), if work permits I will re-write it for S&P.
Marc