Unfortunately, this writeup is a bit of a spoiler. Skip it if you intend to be surprised by the movie.
There was a scene cut from the movie which I felt explained the the fact that the gangsters were behind on the rent extremely well. I almost missed it, and how it explained so much in the movie, until I saw it on the DVD version.
Apparently, the businesses of the gangsters were not making money as well as they needed them to. They were talking to an accountant (who was new, since their old accountant had died) who was telling them that they might have to declare bankruptcy. None of the mafioso could accept the concept. They kept talking about how their businesses should be doing well, etc. And they kept talking about completely unrelated things.
Apparently, they were stuck in their old world and unwilling to accept the new one. Somewhat of the point of the movie, and the cut scene just would have explained it so much better.
But, one of the important concepts of the movie was how these people were anachronisms. And the main drive of the movie was how this girl had her trust fund, which was the gangster's only source of REAL money. And how Ghost Dog got himself in trouble, by killing the guy who was making off with that money.
The whole movie gelled with that scene. I imagine if I watch the movie again, I'll see some more themes in the movie. You're totally right, though. You need to ignore some of the "silly stuff" ... And see some little subtle things in the movie. Like how the gangsters are always watching cartoons -- and how Ghost Dog's assasinations are always foreshadowed by the cartoons that the gantsters watch. (That's what was so silly about that drain-killing... It was taken from the cartoon that the guard was watching.)