I remember a police officer telling me they like getting warrants for small things. For example, if they have a bait car they're trying to get someone to steal they'll have a purse in there. If they can get a warrant that lets them search for a purse (or something the equivalent size) they can basically search everything in the house (anywhere a purse could be hidden), which means free reign to search all drawers, etc. Then anything they find in that search (drugs, etc) can all be used against the person. But if you're only looking for something big (like if someone stole a big screen TV) you're not allowed to search places that it can't possibly be hidden.
But of course I am not a police officer and this was all casual conversation, so grain of salt you know?
I took Navy Security Forces training years ago and our instructors were all ex-cops. They said the exact same thing. It was basically all a big game to see how you could trick or manipulate the "suspect" into letting you violate their rights. Still makes me angry.
You're off a little bit, though this is a HUGELY unclear area in law right now. The term is the "plain View exception" or "plain view doctrine." It's why your trash is searchable if you put it out for pickup. It's why your trash is searchable over a fence if the lid is off.
Horton v. California, while executing a narrowly issued warrant, officers found additional evidence "in plain view" and the Supreme Court ruled the evidence admissible.
The "plain view" issue is one reason to never, ever let a police officer into your house without a warrant. Especially since it can be hard to know what they will claim to be evidence of a crime any more.
They can't keep searching after they find what they're looking for, but if they notice something else while they're there, I think it's okay in the eyes of the law.
