Hi Jim,
I like your tag line, where you give us Jim's inner journey: "to become a mensch". Do incorporate it into the logline as it would make it stronger.
It is not entirely clear to me what the genre is but I assume comedy?
I find it helpful to break down your logline in its parts to analyze:
"Down and out L.A. "Jewish" Attorney can't get a break"
Not sure if you need to include both 'down and out' and 'can't get a break'. The fact that he can't get a break is probably the reason why he is down and out. The logline would be tighter by leaving out one or the other. And it's only setting up the opening situation, I suspect.
"and he bends the rules and "
Here you will need to be more specific. "Bending the rules" in se doesn't sound very interesting. It doesn't indicate what his objective is, either.
"his life takes a fast turn through a dark world."
This is really too vague. It doesn't tell us what exactly he is up against. In order to distinguish your film from hundreds of other movies with characters entering a 'dark world', you need to clarify what it is about.
It sounds like this could be a great film if it delivers on your promise but you'll be able to sell it more easily with more detail in the logline.