Generally my experiences have been positive. The odd speeding ticket, which I deserved, plus two separate incidents when I thought a burglary was in progress and a patrol car was there (lights flashing, no siren) within a couple of minutes (both were false alarms).
One good example of "discretion" I remember from my student days - One summer evening, a couple of us were transporting a keg of beer from one side of Cambridge to another in a shopping trolley. Halfway through the trip (which was hard work and guaranteed to generate a thirst) a couple of bobbies pulled up in a panda car.
"Oi! Where do you think you're going with that?"
"West Road, officer"
"Well just make sure you take that shopping trolley back where you got it."
"OK, we will". And off they drove.
More recently, while living in Australia, our house was burgled during the daytime when no-one was home.
A cop arrived to take a report for insurance (British, as it happened - there's a lot of them in the local police over here).
He asked if I'd noticed anything unusual that day ("looking for clues" I supposed at the time).
I said not really, except we'd had two new wheelie bins delivered that morning whilst everyone was out. Maybe that had some bearing.
He replied "well I'm not going to write that down".
I wasn't expecting they'd go rushing round to the wheelie bin depot, break down the door and shout "You're Nicked!", but with all the stuff about "intelligence based policing" these days, I'd have thought it was a detail worth recording in case there was some pattern (i.e. delivery blokes drop off a bin, house is unoccupied and looks an easy target, one of them makes mobile call to mates with the address. . . .)