Spoilers***Why didn't the bad guys just
shoot Mel Gibson? I can get around the poisoning fiasco of his daughter and not shooting him at the murder scene initially. No need to up the body count unnecessarily.
But then when things are going to hell, everyone connected with the incident is dying and they end up poisoning Mel Gibson. There were a million chances to shoot him and it would have confirmed the original thought: that Gibson was the target and his daughter an innocent bystander. Case closed. No investigation of the nuke plant.
By poisoning him, the coroner will start investigating: the very reason they had to shoot the daughter in the first place. Large plot hole.