This diary is based on general principles of criminal law, the sort of principles tested on a bar exam.
If someone enters my store and tries to leave without paying for a store item, I have no right to shoot him.
If someone enters my store, roughs me up, and takes from the store a store item without paying for it, I have no right to shoot him if I see him later.
A cop has no right to shoot someone unless (a) the cop reasonably believes the person presents a risk of death or serious bodily injury to someone, or (b) the cop is trying to apprehend a suspect the cop believes has committed a dangerous felony (murder, kidnapping, armed robbery, rape, arson, etc). Mere theft (e.g., shoplifting) is not a dangerous felony. Neither is robbery (forcible taking from an individual) when no dangerous weapon is used. Nor is burglary (breaking into a building to steal an item) if no dangerous force is used.
Michael Brown may have stolen some cigars. May have roughed up a shopkeeper. May have been disrespectful to a cop. He was shot six times, twice in the head, at some distance from the cop who shot him He was unarmed.
The correct answer here, based on the facts and law presented, is that the cop had no right to shoot him.