Just had a case with the twist where the police haul some poor sod off as the perp. As it turns out, that person was innocent. In the case closing, I was told that the person was very grateful to me for clearing their name.
I know most of the twists are there for "colour", but I thought it would be nice if this oh-so-grateful person would throw me a little extra reward. Maybe some more experience points (based on the level of the case), or a few extra dollars; nothing huge. And since the twist you get is basically a crap shoot, it can't (I think) be exploited. Also, sometimes that person does turn out to be guilty, so you wouldn't get the extra reward every time you got the twist.
Just a thought.