How soon after the Apocalypse War are you running the campaign Steve? The Apocalypse War happened in 2104. Most of Mega-City One was in ruins afterwards, and millions were homeless, setting up more makeshift shanty towns in and outside the walls. Judge McGruder, head of the SJS, took over as Chief Judge. She stayed in power until 2108 when she took the Long Walk and Judge Silver became the new Chief Judge.
The Justice Department was at an all time low for number of judges and they starting rushing people thorugh the training, hence the "lesser quality" judges who are more prone to corruption.
The city was gradually rebuilt over the next 2 years, but many parts were still in ruins, and irradiated Sectors (or Rad-pits) were dotted around the city. Disease was a common hazard, and pollution was not diminished by tough laws. Unemployment reached nearly 90%, and many bored citizens turned to crime, often just for something to do. A wave of insane crazes swept the city, inspired by controversial vid shows and renegade Juve gangs.
I hope that helps. If you can pinpoint a more firm timeline, I can look through my graphic novels for more details. I would imagine that a lot of the technology would be reduced... for example the Mech Judges have not been designed yet. Dredd has not been to Oz yet, Necropolis has not happened, I believe Orlok the Assassin is currently on the loose... though his name has always bugged me since he is more of a mass-murderer than an assassin.
Anyway, tell us more.