A hotel certainly could search your belongings if that was agreed upon before paying for the room. Mount Olympus Water park in Wisconsin Dells has almost TSA level security* looking for people smuggling in their own water bottles so you'll have to buy drinks from them, and you're forced to walk literally right through the middle of the tourist shop before getting to the rides.
*You don't remove your shoes, but they will dig very thoroughly through any bags or backpacks you are carrying.
Don't like it, just go to the water park across the street (Noah's Ark). More expensive, but less crowded.
As to illegal activity (drug deals, etc.) in hotel rooms, no they don't spy on the inside (at least they better not be) but often there is a suspicion of what is going on when a room has a visitor every half hour that only visits for a few minutes....I wouldn't want to be in that position, because yeah there is a strong suspicion, but it's not exactly proof that something illegal is really happening, and if it is something innocent and the cops got called the customer is going to be pissed! (well, if he was doing something illegal and got arrested he will be pissed too, but at least he deserved it).
My parents used to own a small motel in a small town, 30 years ago. Back then you had to fill out a registration card (name, address, etc.) and put your license plate on it. Most didn't know their own plate # and would have to go check, or they would kind of guess or try to get by with leaving that spot blank. The guy yelling at my dad accusing him of trying to look at his license plate, yeah, that was suspicious.
'Suspicious activity' I've been on both ends of it, seeing someone do something but turned out to be nothing, and I've done something that was innocent that had someone call the cops on me.