When the audience first meet the inspector they know straight away he is an unusual policeman. The name 'Goole' could be a play on words after 'Ghoul' or 'Spectre' also means ghost implying the inspector (who is about to deliver a haunting message) isn't quite human.
The inspector is the central figure yet remains a mystery. It could be interpreted that the inspector is a supernatural coming back to seek revenge for Eva Smith's life and death; a manifestation of conscience revealing each of the characters' weaknesses and guilty secrets.
"Come along, Mr. Croft, what happened?"
The inspector could be perceived as prophetic - has the power to see into the future and knows everything about each character before they speak. The audience learn about Eva Smith through the inspector although his true identity is never revealed which enhances mystery.
The audience find it interesting how the inspector treats the older generation different to the younger generation. The younger generation appear to take the inspector's warnings seriously whereas the older generation see them as a joke.
"The worst part is. but you're forgetting one thing I still can't forget. Everything we said had happened has really happened. If it didn't end tragically then that's lucky for us. But it might have done."
This shows that the younger generation are going to change for the better because they have been affected by what has happened and are thankful the inspector was not a legitimate policeman so they will change from their airs and graces. However, the older generation are not going to change because they are only thankful he was not a policeman so that Mr. Birling could receive his knighthood.
The inspector often tells the characters to "settle things afterwards" this could be in order to make sure the conversation is going in the direction he wants - his lack of time could be because he knows the real inspector is coming shortly - and imposing himself on conversations; this...