Originally posted by Carole Lupin:
It just means he was either the most responsible Dumbledore could find, or that he never got caught.
We know as you said, Dumbledore was hoping he would have some control over his friends, but I am sure Dumbledore knew better. I think part of Dumbledore's plan was to help Remus with feeling like he was worth something, that his life had some meaning.

I think Remus probably suffered knowing with the anti-werewolf sentiment and the registry, he wouldn't be good for much when he graduated. Being made a prefect could have boosted a fragile self-esteem or at least Dumbledore hoped.

As far as getting caught, though I am not sure to what you are referring, we know they never got caught running the grounds. Dumbledore didn't know the other three were Animagus and running around once a month with Remus in werewolf form until the end of PoA when Sirius confessed all.