Audio problem: When Patrick Bateman is exercising and watching The Texas Chainsaw Massacre, the audio does not match up with the actual film. (00:37:05)
Visible crew/equipment: When Patrick Bateman is showing Detective Kimball out of his office, the boom microphone can be seen poking into the shot on the other side of Bateman's interior office window. (00:36:46)
Continuity mistake: When Patrick Bateman murders Paul Allen, the collar on his raincoat is either up or down, depending on the shot. (00:27:49)
Answer: The situation is intentionally left vague. The homeless man being murdered wouldn't necessarily make the news in the time (there were over 4000 murders in 1989-90 when the book and movie are set). He and his friends are so alike that they continually mistake each other for others. The prostitutes would likely be loathe to call the police because they might be arrested themselves and he would likely get off with a much better lawyer.
Greg Dwyer