James Doohan lost a finger on D-Day at Juno Beach.
It's unclear as to where Montgomery Scott lost his...
Here is a still shot of Scotty's right hand from the 1967 TOS "Cats Paw" episode and another from 1967's "The Trouble with Tribbles.
" You can also see his right hand clearly at 19 mins 10 secs (Star Date 3498.9) in the 1966 "Fridays Child" TOS episode .
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If you count the movies, you can clearly see the space where the missing finger would have been when Scotty reaches out to shake the plexiglass plant owner's hand in Star Trek IV: The Voyage Home .
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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.
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You can see his missing middle finger of his right hand in the original series episode " The Corbomite Maneuver " as he reached for a beverage pitcher.
This can be observed in that episode at 8:28 on disk 4 of the remastered DVD.
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Also in "The Lights of Zetar" from season 3
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We were just discussing, in the SF&F chat room here, that James Doohan was missing a finger, but there's no reference to this and I remember watching the series over and over, whenever I had the chance, up through the 90s.  I don't remember ever seeing anything to tip me off that he was missing a finger.  Are there any shots in any episodes of the original  Star Trek  where it is clear he has a missing finger?
Is James Doohan’s missing finger ever noticeable in Star Trek?
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James Doohan lost a finger on D-Day at Juno Beach. You can clearly see the space where the missing finger would have been when Scotty reaches out to shake the plexiglass plant owner's hand in  Star Trek IV: The Voyage Home.  You can also see his missing middle finger of his right hand in the original series episode " The Corbomite Maneuver " as he reached for a beverage pitcher. In Star Trek IV: the Voyage Home and in the Corbomite Maneuver we can see clearly evidence of the missing finger.
In Star Trek IV: the Voyage Home and in the Corbomite Maneuver we can see clearly evidence of the missing finger.