The two incidents you mention did not result in any criminal convictions at all. The judge heard and disregarded all that as non relevant.
The assault on a 'cop' ...was in fact heard at trial. There were undercover cops, not wearing badges, who were in a bar to get underage drinkers. Something about the way they operate undercover had to do with the operations of creating a scuffle in order to provoke and remove - however it was explained, the judge understood. Zimmerman went to the defense of his friend who he thought was being roughed up by some guy in a bar - he never knew it was a cop and the assault was in fact a 'shove' - not a punch or attack. That's why he got a diversion and no other charges were ever filed.
As to the second - there were allegations but they both made the allegations against one another - nothing went to court, nothing was proved on either side and no conviction for any violence, no evidence apparently of any violence on either side. They went their separate ways and that was it.
sammieswife
In 2005, Zimmerman was charged with assaulting a police officer and resisting arrest, after shoving an officer while a friend of Zimmerman’s was being questioned about underage drinking. The charges were reduced, then dropped when Zimmerman entered a pre-trial diversion program. Also in 2005, Zimmerman’s ex-fiance filed a restraining order against him, alleging domestic violence. Zimmerman requested a reciprocal restraining order. Both orders were granted. The incidents were raised by prosecutors at Zimmerman’s initial bond hearing. The judge described the incidents as “run of the mill” and “somewhat mild” and rejected the prosecution’s claim that the incidents demonstrated that Zimmerman was violent or a threat to the community.