Holmes uses the above skills to solve the mystery quickly and efficiently. His astute nature leads him to conclude that Wilson is motivated by money, and has been targeted by the criminals using this. He has been swayed to take Spaulding on as an assistant by the meager wages he can pay him –
I know very well that he could better himself and earn twice what I am able to give him.
Holmes also sees that the Red Headed League is designed to appeal to Wilson’s avaricious tendencies too. The position is outlined as -
...a couple of hundred a year, but the work is slight, and it need not interfere very much with one's other occupations.
Holmes’ observant nature means that he recognizes Vincent Spaulding as John Clay by the acid scar on his forehead. He also notes the dirton Spaulding’s knees when he calls at the shop, indicating that he had been working on th ground and not developing photographs as he said.
Conan Doyle further highlights Holmes skills by showing how, in comparison, Watson is baffled by the case-
Here I had heard what he had heard, I had seen what he had seen, and yet from his words it was evident that he saw clearly not only what had happened but what was about to happen, while to me the whole business was still confused and grotesque.