Always one of the least realistic aspects of the D20 system, going way back to First Edition D&D has to be Hit Points. The standard arguement is that they do not represent just physical damage but also exhaustion and the ability to turn a blow into a less serious one.
It gets harder to justify though as characters get higher in level. I remember a more realistic system in Cyberpunk 2020 had characters having to make what they called a stun/shock save every time they got hit in order to stay conscious ! This sort of thing probably would not work in Judge Dredd though as you wouldn't want your judges taken down so easily.
Stepping up the damage dice is one idea, and I will definitely consider it before I play. But I like to try and keep my D20 games relatively low powered so I don't need to do this. Judges start at lvl 3 so they have an automatic advantage in HP ( as well as their impressive armour ). Most of the perps they meet will never be more than lvl 1 though so the 3D6 damage from a lawgiver will easily take them down with one shot ( never mind the chances of doing even more with a critical ). As the PC's reach higher levels rather than stepping up the levels of the NPC's the perps shoud still only by lvl 1 on average, but there can be more of them ( a riot or a block war should provide enough lvl 1's to challenge even a high level judge like Dredd ). Only the main bad guys need to have higher HP as you want to keep these alive longer, and they should be noticeably harder to take down.
So, while I agree that damage needs to be more deadly I'm hoping I can do this by keeping the levels of both PC's and NPC's relatively low. When ( if ) the PC's do get to the dizzy heights of Senior Judge at 12th level then the average lvl 1 juve is going to be no problem - its the dark judges and the like that the PC's will have to worry about instead.