He seems to know and understand an extraordinary amount:
He knows the history of Eva Smith and the Birlings' involvement in it, even though she died only hours ago. Sheila tells Gerald, "Of course he knows."
He knows things are going to happen - He says "I'm waiting... To do my duty" just before Eric's return, as if he expected Eric to reappear at exactly that moment
He is obviously in a great hurry towards the end of the play: he stresses "I haven't much time." Does he know that the real inspector is shortly going to arrive?
His final speech is like a sermon or a politician's. He leaves the family with the message "We are responsible for each other" and warns them of the "fire and blood and anguish" that will result if they do not pay attention to what he has taught them.