When Ma-Ma asks Dredd if he "like[s] the jewelery" and reveals the transmitter on her left wrist, the shot cuts to Dredd, who turns slightly to look at it. However, he turns to his own left, as if Ma-Ma had the transmitter on her right wrist.
Near the end of the movie, when the blast door opens, Dredd and Anderson are standing side by side waiting. Seen from the front, Anderson is holding an assault rifle, and Dredd isn't holding any weapon. Then in the next shot, seen from the rear, Anderson is still holding a rifle, but Dredd is now holding a pistol.
At 1:14:30, Dredd checks down a litany of ammo types, trying to find one that the gun isn't out of. He checks Rapid Fire/RF, Incendiary/IN, & Armor Piercing/AP. Two of these names are visible & have 0 levels showing in the led readout, and the (type obscured) readout is probably Rapid Fire. When he calls for High Explosive/HE, suddenly readouts for all ammo types show 25 rounds each ammo remaining, and the readout for (type obscured)RF, probably, reads 50.
After being shot by Judge Lex, Dredd administers first aid to the wound in his stomach. This wound is considerably bigger than the hole the bullet made in his body armour, plus he completely ignores the matching wound in his back.
When Dredd and Anderson first arrive at Peach Trees, Anderson explains that the reason for not wearing her helmet is that it interferes with her telepathic ability. This is further demonstrated when she fails to read Dredd's mind on several occasions. However when she confronts a helmeted Judge Kaplan she is immediately able to determine that Kaplan is one of the bad guys.
When Dredd and Anderson approach a group of 10 thugs outside the Medical Centre, Dredd throws a stun grenade. As the camera tracks the grenades progress across the floor, the wire used to guide it is clearly visible.
In the flashback scene showing Ma-Ma's opposition being killed, one man who is obviously alive and conscious is thrown down on the ground and shot several times in the back. As the bullets strike, he doesn't flinch from the impact.
The goof items below may give away important plot points.
When the block goes into lockdown, the blast door comes down and crushes the vagrant right in front of Dredd and Anderson. At the end of the movie, when the blast door goes up, there is no sign of the body.
When Dredd and Anderson first arrive at Peach Trees, they call for some wagons to take away dead bodies and a suspect. No one shows up and control doesn't try to figure out why the judges haven't filed a report yet. Then there is a convenient security system check without any record of authorization right after a call from the judges for the wagons.