That term is used if there is no temporary injury which is detrimental to a person's health. Here we're talking about assault with bodily injury. Assault with bodily injury is more than just an ordinary injury; it's an injury that is prejudicial to one's health and is not of a temporary nature. For example, it could be a scar or a large bruise. As you say, it could involve pushing someone, or making him fall, but without actually hurting him. If the person is not hurt, there is no bodily harm. Often, it's a matter of coincidence whether a person has injuries or not.
We can certainly discuss the differences here, but as far as the police are concerned--and I want to make it perfectly clear that I am not criticizing them--it's different. When the police arrest someone for assault, it doesn't matter whether it's common assault, assault with bodily injury or aggravated assault. The important thing is to stop the assault. For the investigator, that may be more important, but as far as the police officer is concerned, that difference is not so important. His responsibility is to prevent someone from hitting someone else, for example.
As regards authorized offences, I would limit them to offences with a judicial warrant that are clearly framed. The police asked that section 25.1 be added following the Campbell ruling by the Supreme Court, which said that the controlled sale of narcotics is illegal and constitutes a crime, even if it is carried out by police officers. The police reacted by requesting general immunity, when Parliament had already passed specific provisions relating to the controlled sale of narcotics. In fact, those provisions still exist.