MAROON: Look, Valiant! His wife's poison, but he thinks she's Betty Crocker. I want you to follow her. Get me a couple of nice juicy pictures I can wise the rabbit up with.
Jessica has a bad reputation mainly because she's an attractive woman. Men don't trust her, probably because they're jealous of Roger, so they spread rumors to harm her reputation.
LT. SANTINO: Gee whiz, Eddie. If you needed money so bad why didn't you come to me?
While we're not sure exactly why Eddie quit being a cop in order to become a private detective, we can reasonably assume that Eddie had noble intentions. Since the death of his brother, Eddie has had to turn to sleazy jobs to pay the bills, and these gigs harm his reputation.
OFFICER: Didn't you used to be Eddie Valiant? Or did you change your name to Jack Daniels?
Being an alcoholic doesn't help Eddie's image either. We have to wonder if he's screwed up any cases due to being drunk.
JESSICA: I hope you're proud of yourself, and those pictures you took
In case you needed one more reminder that Eddie is doing shameful work, Jessica is here to drive the point home with a vicious slap on the cheek. Eddie needs it though to snap out of his funk and get motivated to redeeming himself.
VALIANT: Ain't my fault the rabbit got himself in trouble. All I did was take a couple of lousy pictures.
Eddie tries to talk himself out of his guilt, and convince himself he's just doing his job. But he realizes that the job he's doing is a sleazy one, and he's hurting people more than he helps them.
ROGER: You're also the guy that helped all these Toons. Everybody knows when a Toon's in trouble there's only one place to go. Valiant and Valiant.
This is the line that proves Eddie didn't always have a bad reputation. In fact, he used to have a good reputation as a hero for the Toons until one murderous Toon ruined the reputation of all Toons in Eddie's eyes.
DOLORES: I thought you said you'd never take another Toon case? What, did you have a change of heart?
VALIANT: Nothing's changed. Somebody's made a patsy out of me and I'm gonna find out why.
At first, Eddie's reasoning for turning himself around is a selfish one. He wants to prove to himself that he's a good detective. He'll do some real good along the way, almost by accident.
JESSICA: I'm not bad. I'm just drawn that way.
A person's reputation is often judged by their appearances. Someone in a leather jacket is trying to be cool. Someone in hemp pants is a hippie. And beautiful women often get reputations among men for being troublemakers. Consider this Exhibit 3,456: People Are Terrible To One Another.