The Korob and Sylvia alien puppets at the end have obvious wires. The wires are digitally removed in the remastered 2006 version.
When Kirk, Spock, and McCoy beam down, they're far closer together than the transporter pads on the ship.
Made as a "Halloween Episode" with an
abundance of Halloween themes and imagery, such as castles, black
cats, dungeons, skeletons and so forth.
The skeleton next to McCoy in the dungeon has a seam on its skull where it had been sawn open. This seam is typical for medical skeletons.
Kirk comments that they can easily make gems and dismisses Korob's bribe. In
"Arena" he finds some diamonds and described them as being a vast fortune.
James Doohan's missing finger can be
seen (if that makes sense) when Scotty is holding the phaser.