I would think that the fact that Treyvon had apparently been in trouble for fighting before would be relevant when the key point in Zimmermann's story is that the young man jumped him and began pounding his head on the ground. It shows a propensity on the part of the victim to resolve confrontation by means of physical assault.
That may arguably be true if Zimmerman knew of Treyvon's propensity for violence, but then he could testify to it himself. There's no need for others to testify to what was in his mind. It's likely irrelevant anyway. If he was reasonably afraid of being assaulted at that moment then it wouldn't really matter whether the person he shot had ever committed an assault prior or not.
P.S. I know nothing about this case and did not pay the slightest bit of attention to it, I'm just bringing up general points of law.
For what it is worth, I have testified in a quite a number of homicide, rape and armed robbery cases, sometimes as an "expert witness" sometimes as a "fact witness."
What Rev says here is true in practice, at least in the courts in which I've testified.
Very, very rarely in any felony case is the 'past' of the defendant (or in cases like this one, the victim) admitted. It simply is not relevant in the vast majority of cases. The only fact that would matter is if the person who did the killing was in fear for their life AT THE TIME OF THE KILLING.
Further, the jury (or court in general) can only judge the situation by the fact known to the actors at the time. You cannot use hindsight...which knowing the victim's past would likely be.
The relevant case law, at least in terms of deadly force involving police, is Tennessee v Garner (1985). I think it was not the main issue of contention in that case, but I'm pretty sure that was the case where the court specifically stated that facts known to the actors at the time of the incident are the only facts relevant at trial. Rev, can you correct me on that?
The other thing I don't know is if Tennessee v Garner is the applicable law in civilian deadly force cases. Rev, any idea on that?
The bottom line, and the argument I have heard countless times in felony trials, is that presentation of past criminal activity is deemed prejudicial...jurors MAY make assumptions of guilt based on knowledge of past behavior rather than deciding THIS CASE.
Rarely, past events are allowed, but even then, they are generally allowed only in a very narrow scope...such as if Zimmerman and Martin had had a previous confrontation, and then it would likely only be to the extent of "Was a police report filed...if so, how was that adjudicated?" Very cold, factual presentation of documented, "official" facts would the limit.
There are notable exceptions, too. For example, in 'three strikes' type cases it must be shown, and recorded, that past convictions occurred. So, for example, if a person was on trial for second offense of something, very clearly it has to be shown they have a first offense, or legally the jury can NOT find them guilty of second offense.
Finally, think about it this way. Not only does excluding Martin's past protect Martin, but it protects Zimmerman as well. If the court were shown that Martin had a violent past or a propensity to solve disputes with violence, then it MAY be argued that Zimmerman went into the situation fully expecting not only violence but planning deadly force. Painting a character one way gives the other actors "motivation" they may or may not have had, at least in the minds of the jurors.
Does that last bit make sense?