I actually agree with Pappy. Even if Trayvon is a scumbag, it doesn't give Zimmerman any more right to kill him. I think that introducing all of these other things only helps the prosecution's narrative. As the defense, you're not trying to make the case that Zimmerman killed Trayvon because he was bad. It was that he killed him because he had to in order to protect his own life.
You're forgetting something: it's easier to convict someone who the jury hates (even if the facts aren't terrible) and it's easier to lose a conviction if the jury likes someone (even if the facts are pretty damning).
If the jury hates Trayvon, then, even if the facts against Zim are pretty bad, that'll weigh in Zimmerman's favor. If the jury hates Zim, then, they'll likely convict him, even if the facts against him are only mediocre.
Two points: One, the prosecution can't bring up past bad acts, generally. They can't have someone come in and say that Zimmerman was a thief and liar. However, they can bring in "pattern" evidence. So, if he has a pattern of violent acts... that may be able to come in. The trouble is, if the defense puts up some testimony that Zim's a good guy, and wouldn't hurt someone, then, that opens the door for the prosecution to respond.
Two: I would be really interested to see if anyone makes a Batson motion in this case. If someone strikes a juror on the basis of race or gender, and can't give a race- or gender-neutral reason for the strike (negative law enforcement contacts, bad guy, appears unable to focus, blah, blah, blah) then, they lose that strike and the juror they struck can be empanelled. That'll be a show, I promise you, given the racial overtones of this case.
My bet: end of the day, unless Zimmerman has some very strong evidence that leads people to believe that he shot the kid because he was being attacked (and he might, given his scarred up face on the night of the killing) the jury will convict on a lesser included offense than the one charged. Maybe manslaughter or something.