I'm not an attorney, but I believe for the police to make an arrest of the girl, the pot would have to be out in plain sight. They can't use evidence they find in a search when it doesn't relate to the case they're working on. Again, I'm not a lawyer so you'd have to double-check this.
It's incorrect.
If the search is legal in the first place, then as a general rule, they can use anything they find. Like, if the cops have a warrant to search a house because they think the person living there is a burglar and has stolen goods in the house, and then when they search it they find drugs or a dead body, they can certainly charge him with drug possession, murder, etc. The same goes if they're invited into the house by the owner (that's how Boy George recently got sentenced to community service for drug possession: he called the cops to report that things had been stolen from his apartment in New York and let them in to investigate, but they found drugs while they were there.
But
if the search is illegal, (e.g. no warrant, no crime in progress [if a crime is actually in progress they can go in], the owner doesn't voluntarily let them in, etc.), then they can't use anything they find for the case they were investigating or any other case.
I'm with Vanatru however; I doubt the police are going to make much of an investigation at all unless they're called in my one of the humane associations. I had a $2000 mower stolen once; the police response was to give me a crime report number over the phone to use to file with my insurance. That was it. There's only so much they can do.
Yes, I agree completely. For small things like that, the police generally won't investigate much or at all. And in the example of the girl with the cat killed, even if they DID investigate, I can't imagine why the cops would ever set foot in her bedroom, since it has nothing to do with the crime. (I'm assuming that's not where the cat's body was found--I'm picturing the 16 year old at home in her room, and the cat being killed elsewhere in the house or outside.)