Quote from tomdavis:
As a general rule, anti-propensity doctrine prevents the prosecution from presenting evidence of a defendantâs "bad character" because our system of justice does not want a jury convicting a defendant for being a bad person when, in fact, he or she is on trial for some specific crime -- in this case murder. If prosecutors could present a case made against the "character" of the defendant they would be telling the jury that this is a person who should be punished irrespective of whether or not he was actually guilty of the alleged crime.
What gets presented in the courtroom is up to the judge, but a character assassination that's not directly related to the commission of the crime probably will not see the light of day. If Zimmerman were charged with defrauding Martin, then a pattern of lies would be relevant; but in a murder case I doubt it.
The yet to be created jury already knows this; no need to include at trial.