Can the rest of us get us one of them thousand foot gun free perimeters?
There are two things 'wrong' with this.
1) 'get us' - where get is reflexive, we'd say "get ourselves", not "get us".
2) 'one of them' - should be 'one of those'.
I haven't seen the clip, but knowing the Daily Show, it's important to understand that John Stewart wasn't 'trying to sound uneducated' (as Robusto has it); rather, he's mocking the uneducated by caricaturing how they might speak. My guess, given it's relating to gun control, is aping how a Texan red-neck might speak if he ever realised that gun ownership is ridiculous (I'm not stating my view; this is what Stewart is implying).
People do sometimes use 'them' for 'those' to appear less educated than they are, but this is not Stewart's intention here.