Here's what the Sanford police should have done. (P.S., trust me on this one, I know what I'm talking about.)
1. Immediately canvassed the entire neighborhood to locate any persons who might have, within the previous hour seen or heard Trayvon, Zimmerman, or any signs of a struggle.
2. A wider search and canvas should have been done to locate the residence of Trayvon.
3. Immediately seized Zimmerman's firearm and held it as evidence.
More below the Squiggle of Doom.
4. Zimmerman claimed he was in some kind of struggle with Trayvon. Whether this occurred in a grassy area, or simply an area of dirt or asphalt, there generally will be material transferred from the surface (bits of asphalt, dried plant particles, etc.) to the clothing of the person in question. This can either support or defeat a story. Zimmerman's clothing consequently should have been seized for evidence processing by the crime lab.
5. For the same reasons, Trayvon's clothing should have been seized and taken to the crime lab for analysis.
6. Similarly, the surface areas (asphalt, grass, etc.) should have been closely inspected for any fabric or items such as button that might show where there had been contact with someone involved in the matter.
7. Zimmerman claimed he had an injury as a result of being attacked by Trayvon. Zimmerman should have been examined by medical personnel to determine a possible cause and recency of the claimed injury.
8. Zimmerman should have been asked to submit to a blood test for drugs and alcohol.
9. Zimmerman should also have been asked to consent to search of his motor vehicle. Such a search might have disclosed implausibilities in his story, such as his claimed need to examine a street sign, which caused him, he says, to have to exit the vehicle. If Zimmerman had reentered the vehicle following the purported struggle, one would have expected trace evidence to be transferred to the interior of the vehicle.
10. A detailed three-dimension reconstruction of the crime scene should have been made, using as reference points the wound or wounds sustained by Trayvon, the position Zimmerman claims he was in when he fired the weapon.
11. Presumably Trayvon still had the Skittles packet in his possession and an energy drink, I believe. A reasonable deduction would have been that Trayvon had recently been to a nearby convenience store. The police should have immediately contacted all the convenience stores within walking distance to determine whether and when Trayvon could have been there. This could have led to a more rapid identification of Trayvon's body.
12. The failure of the police to follow up on the numbers on Trayvon's cell phone has as been widely commented on. Had they done so, they would have been immediately led to a witness, the girl to whom Trayvon was talking at the time of the incident. Additionally, the fact that Trayvon was talking on the phone might readily have discredited Zimmerman's story.
Now, some of these steps may have been taken. But it seems clear that others certainly were not. This is basic police work. I can guarantee you that had it been a 17 year-old white boy shot down dead, everything I say here would have been done.