The reason you don't remember Scotty missing a finger is that Scotty, the character, is not supposed to be missing a finger. Any scene where you can see the missing finger are filming goofs. Close-ups of his hand were filmed using a hand double.
Eddie Paskey, who played TOS background character Lt. Leslie, stood in for Doohan for some episodes requiring closeups of Scotty's hands.
From Memory Alpha:
He was the hand-double of James Doohan in "Wolf in the Fold" and "That Which Survives". Doohan was self-conscious about the fact that he was missing the middle finger of his right hand (due to a D-Day combat injury while serving with the Royal Canadian Artillery), so Paskey's hands were used in close-ups.
Screenshot of Scotty's Hand Doubled hand from TNG Relics:
A list of filming errors from wiki:
Despite his efforts, the injured hand can be seen in several Star Trek episodes: "The Trouble With Tribbles", "Tomorrow Is Yesterday", "The Enemy Within", "The Ultimate Computer" and "Catspaw", as well as in The Search for Spock when giving parts from the USS Excelsior to Dr. Leonard McCoy, in The Final Frontier when Nyota Uhura brings him dinner on the bridge of the USS Enterprise-A, and in the Star Trek: The Next Generation episode "Relics", when the missing finger is clearly apparent as Scotty offers Captain Jean-Luc Picard a drink while on a re-creation of the original Enterprise bridge.