The detail about razor blades found in candy is brilliant because it merges the fictional Candyman figure with a very real and well-known urban legend - the dangerous Halloween candy. The fact that the perpetrators were never caught also adds a bit of realism, as in Real Life, the razor blades was often put in the candy by family members. Thus it makes sense that Sherman Fields was just a scapegoat for the authorities, who didn't want to deal with the more horrifying realities of the urban legend.
When Anthony and Burke first meet, Burke snaps his fingers as he pulls his hand away. Snapping fingers when you remember someone or something is a common gesture. Given how everyone in Cabrini Greene knew the true story about Helen and the Candyman, it's easy to assume that Burke knew who Anthony was after the latter gave his name.
Anne-Marie mentions that the only reason why the Candyman started appearing again was because someone mentioned his name and broke the pact Cabrini Greene had about the legend. Burke is one of the first people to call Candyman by his name when he is talking to Anthony during his interview, and he's also the one who tries to turn Anthony into the next Candyman.
