The Bobby Darin version of "If I Were A Carpenter" is used in the soundtrack rather than the Tim Hardin version because of Darin's Italian pedigree, born Walden Robert Casotto. His name is mentioned in the last episode of the show as well.
The trope of falsely accusing black men for things that go wrong (referred to in the title and repeated throughout this episode) is one of many nods to GoodFellas in The Sopranos. One of the first scenes in that film shows a truck driver deliberately letting his truck be robbed by two (white) gangsters, then feigning surprise when the truck is stolen and yelling "Two n*****s just stole my truck!"
"Unidentified Black Males" aired during the 2004 season. If the action was set in that same year, then the events of this episode would have taken place around June 11th-13th, 2004, as those were the three days during the 2004 Major League Baseball season that the San Diego Padres were in New York playing the Yankees.
The song during the closing credits "If I Were A Carpenter" was sung, with different lyrics, by Christopher in "No Show" (S4 E2), which also showed the construction site of The Esplinade with the no-show crew.
Steve Buscemi's limping is a reference to the 2002 Off-Broadway production of "The Resistable Rise of Arturo Ui," where Buscemi's character limps during the course of the entire play. The same production also starred Dominic Chianese and John Ventimiglia, about two years before this TV episode aired in May 2004. His limping is also caused by his foot getting run over in the previous episode.