One of the problems with bucket necks testimony is that it contradicts the argument Martin was running away. The conversation before the confrontation appears to have been subdued and not exasperated as it would have been if Martin were running. Martin also seems to be the one who initiate first contact. Not that initiating contact first is relevant to guilt or innocence.
The bolded is actually very relevant. The Florida Statutes states that if you provoke the use of force against you , you are then obliged to seek all reasonable avenues to escape danger. So if it is deemed that Zimmerman did initiate the fight, then the bar for the justifiable use of deadly force is raised that bit higher
776.041 Use of force by aggressor.—The justification described in the preceding sections of this chapter is not available to a person who:
(1) Is attempting to commit, committing, or escaping after the commission of, a forcible felony; or
(2)
Initially provokes the use of force against himself or herself, unless:(a) Such force is so great that the person reasonably believes that he or she is in imminent danger of death or great bodily harm and that he or she has exhausted every reasonable means to escape such danger other than the use of force which is likely to cause death or great bodily harm to the assailant; or
(b) In good faith, the person withdraws from physical contact with the assailant and indicates clearly to the assailant that he or she desires to withdraw and terminate the use of force, but the assailant continues or resumes the use of force.
http://www.leg.state.fl.us/Statutes/index.cfm?App_mode=Display_Statute&Search_String=&URL=0700-0799/0776/Sections/0776.041.html