Is there a minimum threshold that must be met in terms of intensity for someone to charge another person with breaking the law? For example, if someone (purposefully) shoved someone as a form of aggression once, this would be considered assault. If someone was smoking in a no-smoking area, could you take them to court? Does this mean they can sue them? I think there has to be some damages.
First, only the state, usually through the police or a public officer can take someone to court for a crime. If it is a crime then it is at their discretion if they believe the offence is serious enough to warrant this.
Anyone can take anyone to court for a civil wrong (e.g. Breach of contract, a tort etc.). One of the many things that they will have to prove are damages if they are seeking damages. The defendant can argue in court that there were no damages as part of the defence. A judge will look at the evidence and, if there appear to be no damages they can make a summary judgement either with or without prejudice.
Of course, damages are only one remedy for a civil wrong. To take your "smoking in a no smoking area" example: you could take the person to court to get a court order (an injunction) that they are not to smoke in that no smoking zone again. If they do, then they will have committed the serious crime of contempt of court.