I pretty much subscribe to the "classic" theory that the events prior to the Cowboy's "Hey pretty girl" scene are Diane dreaming. Throughout those scenes, I think we see elements that reflect (in different ways) Diane's wish that she hadn't placed the hit on Camilla. For example:
- There's the beginning of a hit attempt in the limo, but it's interrupted by the car crash.
- There's the scene at Winkie's between Dan and Herb, where Diane's dream returns to the place she hired hit man Joe, but this time it's entirely different (she's Dan instead of Diane... it's day instead of twilight... she "had a dream about this place" instead of this being where she started the all too real contract hit... etc.).
- In the dream, the Castigliane brothers are responsible for the ominous "This is the girl" line, instead of it being the words she used to seal Camilla's fate.
- Ed -- a guy we never see her meet outside the dream -- seems to have been set to kill Camilla, but was thwarted by the car crash.
- Joe -- the guy she does meet outside the dream -- kills Ed, but does so in a way that makes him seem completely incompetent (perhaps reflecting the wish that he'd really been a bumbler instead of a successful killer).
- Throughout the dream, Betty tries to help Rita, rather than trying to kill her.
- ...And so on.
So I think the "careless hitman" scene fits right in with that. If Ed
isn't a hitman, I can't really see him as a PI investigating Camilla's murder, though perhaps he could have been hired to find her. Or -- given the lines about the "famous black book" containing "the history of the world in phone numbers," maybe Ed's racket was blackmail, and he had a blackmail scheme planned against Camilla that derailed when she was in the car crash and disappeared. But really, if it's true that the Ed & Joe scene is part of a dream, Ed's profession probably doesn't matter much.
It could also be that Joe and Ed are another pair of dream dopplegangers for Diane and Camilla. Joe is blond like Diane; Ed is brunette like Camilla. The blond kills the brunette. Joe and Ed seem to be in a similar line of work, but Ed seems more successful (at least he has his own office!) while Joe seems like a loser and a bumbler, etc...