The climax to Thud, without spoiling, relies on the fact that Nobby will pick up anything he finds
There's an unlocked evidence locker in the Watchhouse that Nobby will empty by the end of any given day
I'm pretty sure at one point he's testing front doors to "make sure that they're locked" (I think whichever book Carrot joined the cast?)
I'm not saying he's not a basically good person. Er. Well, whatever, he's not a maniac. And he's not really a MUGGER, per se. He's more likely to take a necklace off a body he finds in the alleyway, rather than actually attacking someone.