The Florida police department handling the fatal shooting of an unarmed black teen by a self-appointed neighborhood watch leader admitted to ABC News tonight that investigators missed a possible racist remark by the shooter as he spoke to police dispatchers moments before the killing.

The admission comes a day after the Justice Department announced that it has launched an investigation of the slaying of Trayvon Martin by George Zimmerman last month as a possible hate crime.

On a tape of one of Zimmerman's 911 calls the night of the shooting, he is heard saying under his breath what sounds like "f**ing coons." Seconds later he confronted Martin and after a brief scuffle shot him dead.

Zimmerman claimed self defense, and was not charged with any crime.

It's the latest in a series of possible police missteps uncovered by ABC News.

The Sanford Police Department has come under withering criticism for failing to reach out to Martin's girlfriend, who was talking to the teen on his cell phone and heard the altercation with Zimmerman take place.

Among other issues, police have been criticized for:

Withholding a batch of telling 911 calls, including the one revealing Zimmerman's possible racist remark.

Sending a narcotics detective to the scene, instead of a homicide detective, as is typical for homicides.

And failing to administer a drug and alcohol test to Zimmerman that night, which homicide investigator Rod Wheeler called a "fatal flaw in the investigation."

"The fact that Mr. Zimmerman was not given a toxicology test or breathalyzer examination is huge. Very huge," Wheeler said. He also wondered why Zimmerman's vehicle was not investigated or impounded.

The Sanford Police Department says it stands by its investigation, and that it was not race or incompetence that prevented it from arresting Zimmerman but the law.

Martin had left his father's fiance's home to buy a pack of skittles at a convenience store. On the way back he called his 16-year-old girlfriend. She was on the phone with him as he told her about a man following him.

"He said this man was watching him," the girl recounted. "So he put his hoodie on, said he lost the man. I asked Trayvon to run, and he said he was going to walk fast, I told him to run but he said was not going to run."

But the man would catch up to Trayvon, she recalled.

"Trayvon said, 'What are you following me for?' and the man said, 'What are you doing here?' Next thing I hear is somebody pushing and somebody push Trayvon, because the headset just fell," she said. "I called him again and he didn't answer the phone."