How does the father figure to go to the old crooked diamond seller?

A lot of people seem to be assuming that, because Charles knew the fence, he must have had some dealings with him. I just don't see the evidence for that - most of their conversation is about how they knew each other because they both started in the business at the same time and in the same neighbourhood, and the fence's whole motivation for revealing Andy as the potential seller is to get back at Charles for his perceived denigration of the fence's illegal activities for the whole length of their relationship. If anything, the exchange suggests that Charles was scrupulously honest in his dealings, as one crook doesn't usually have a whole lot of moral authority over another. The fence was stung by Charles' disapproval precisely because Charles was successful without being a criminal, which contradicted the fence's worldview that criminality was forced on everyone by the world at large. Charles' virtuous example made the fence feel like a lowlife.

Besides, if you work long enough in any industry, you get a sense of who the crooked operators are pretty quickly.

I thought Andy made a stupid move here as well. If you're going to reveal to a third party that you've committed a crime, its a good idea to wait until after the crime has been succeessfully pulled off. Because if it doesn't go according to plan, its just one more loose end you won't have to worry about.

IMHO it was one of the weaker points in the movie though. Had this taken place in some rural town then I could buy that the father would hit the same fence as his son had chosen - but this is NYC. One in a 100 if not 1,000 chance. It would have been more credible, again, IMHO, if the dad had gone to the old acquaintance to see if he could give him some insight/advice as to where the thieves, they possibly from up in the Westchester Co area, might go about getting rid of some hot ice. Just a hairs difference in the dialogue and the fathers characters demeanor when he approached the old fence would have made this scene succeed. IIRC, he went into the store with a hunch that this was the place the thieves went to unload.
"Of all the gin joints .."