Dupin, we admit, is really good at figuring things out. He's also good at criticizing G—. He makes a big deal about how flawed G—'s methods are. He asks the narrator, "Do you not see he has taken it for granted that all men proceed to conceal a letter […] in some out-of-the-way hole or corner [...]?" (98).
The plan G— creates for the search, though, isn't limited to secret places. His plan is to search everywhere:
"We divided its [the house's] entire surface into compartments, which we numbered, so that none might be missed; then we scrutinised each individual square inch throughout the premises, including the two houses immediately adjoining, with the microscope, as before." (55)
Notice that Dupin says they divided up and searched the entire surface. Remember when Dupin suggests that D— has "been making a miscalculation" (68)? Well, this is the miscalculation. He forgets to search the objects in the house that are not on the surface. He forgets to look in the air.
But Dupin doesn't:
"At length my eyes, in going the circuit of the room, fell upon a trumpery filigree card-rack of pasteboard that hung dangling by a dirty blue ribbon from a little brass knob just beneath the middle of the mantelpiece." (114)
The blue ribbon suspends the card-rack, and therefore the letter, in air, and that's why G—missed it. If he and his men had divided the non-surface areas of the house, they would have found the letter. So, it's not G—'s method so much as his calculations. In this way, the blue ribbon is a symbolic clue that helps us compare the detection methods of Dupin and G—.