I don't see why you're giving this particular cop the benefit of the doubt when he's obviously shown he's a complete retard.

The cop can truthfully say "we've had some stuff going on here" about any neighborhood. They can say that whether there's been stuff going on or not. How are you going to know if it was something three blocks away that happened 4 years ago?

Now, for this specific incident: If you see someone sitting on a patio where there's a no trespassing sign, that alone is not very suspicious. You should think 99% chance he lives there or is working there. Then, if you for whatever reason decide it is suspicious (maybe there's a trespassing epidemic going on in that town, who knows), and then go up to him and see he's picking up garbage around the place that should tell you he's 99.999% not a trespasser. He's fucking working, duh!

At that point the cop should have put 2+2 together and said 'have a nice day, sir' and fucked off. Instead he decided to go on a power trip and try to boss the guy around a bit.

Once the cop's committed to his 'investigation' though, it's pretty unlikely, even if he realizes how dumb he's being, that he's going to just stop and go 'sorry my mistake.' The chance he will do that is even less than the chance the guy he's harassing is actually a trespasser. So the kid should have realized it was pointless to argue with Seargeant Shithead and just let him have whatever little orgasm he gets from playing Kojak.