Tools of Characterization
One handy thing about having a first person narrator who's constantly watching the hero of the story is that he's able to tell us blatantly what kind of a person Dupin is. It's from the narrator that we learn that Dupin's an aristocrat who's fallen on hard times, that he's moody and brilliant and bookish, and that he's smug about his superiority over the police. The narrator uses this tool briefly when we meet the sailor, the only other character in the story who actually has his own lines: the narrator describes him as "a muscular-looking person, with a certain dare-devil expression" (102).
Since the primary purpose of "The Murder in the Rue Morgue" is to demonstrate the greatness of using your powers of observation to make exciting deductions, it makes sense that a lot of Dupin's character comes through in the habits that the narrator tells us about. Dupin's interested in randomly speculating about others. We find this out from the fact that he and the narrator like to walk around the streets of Paris looking at people and trying to guess their personalities and thoughts. At the same time, he's not that keen on interacting with said people. We find this out from the fact that Dupin and the narrator like to spend the whole day sitting inside with the blinds drawn and the whole night walking ceaselessly up and down the streets of Paris.
Thoughts and Opinions
We've been describing Dupin as "smug" and we suddenly started to wonder why. Then we realized that it's because, every time he expresses an opinion about the police as a group, the Prefect of Police in particular, or François Vidocq (see "In a Nutshell"), it's always seems to be patronizing and condescending. Dupin has plenty of views about the mental abilities of people around him, and he's perfectly willing to share.