When the three Romulans move in to attack the balloon, the top-most ship is pointed in the direction they're moving: toward the upper-right corner of the screen. The middle ship is facing toward the camera, and the bottom ship is pointed toward the lower-left corner. Despite that, all three ships move toward the upper-left.
During the second Romulan attack near the end, the stars are missing from the lower right 2/3 of the view. Only the top left 1/3 has even a sparse population of starfields.
McCoy repeatedly has/doesn't have a black strap across his left shoulder while treating Kirk and finding a treatment for the plague.
On beaming up from Dramia II, the pad orientation is not the usual circular pattern. It's two sets of three side by side. The people beaming in do not stand on the pads.
When confronting Dramo on first entering the ship, Spock's insignia appears on the right side, instead of the normal left.
McCoy says that the crew are in the terminal stage. But as established earlier red is the terminal stage and Kirk is still green-ish. Later when McCoy administers the antidote to the other victims, they're green as well.
Kirk and Spock both beam down to Dramia II unarmed yet Demos, their prisoner who they'd just arrested for stowing away on the Enterprise, still possessed his weapon throughout the episode.
When Kirk asks Sulu about radiation on Dramia II, his uniform insignia badge is missing.
Kirk orders the hanger doors to be opened so that Demos will sneak aboard. The next shot shows Demos watching the hanger doors opening. Demos then flies straight through the newly opened doors without making any checks. This behavior seems very unlikely, if not stupid.
In the transporter room at the end, McCoy is wearing a yellow shirt in one shot.
in the first appearance of Kulkakan's ship, when it starts to attack the Enterprise, the stars behind it all disappear, leaving total blackness.
In the last appearance of Kulkakan on screen, his teeth/fangs turn green for a couple seconds and then turns back to white.
Kirk consistently mispronounces Ku-KUL-can as "KOOK-lu-can." According to the DVD commentary, this was because William Shatner recorded his voice material separately and author David Wise wasn't present to correct him.
Uhura is drawn as a Caucasian in one bridge shot.
On the DVD release of the Animated Star Trek, some episodes were accompanied by Text Commentaries from Mike & Denise Okuda. The commentary for "The Counter-Clock Incident" contains a rather notable error though. The Okudas comment on Sarah April's Capellan Flower, stating that Capella IV was visited in TOS's episode "A Private Little War," but Capella IV appeared in "Friday's Child". The planet seen in "A Private Little War" was never named on screen, but was referred to in scripts as Neural.
This episode contained a slight chronology error. In an early scene, McCoy says after giving Sarah April a tour of sickbay, "Jim, I didn't realize how many of the tools I use in sickbay were designed by Sarah." To which Sarah replies, "As the first medical officer aboard a ship equipped with warp drive, I'm afraid I had to come up with new ideas all the time." This clearly can't be true, since the Bonaventure, not the Enterprise was the first starship with warp drive installed. She must have meant something like she was one of the first medical officers aboard a ship with advanced warp drive installed.
This episode makes absolutely no sense. So what happens when Karla Four's "father" reaches the point of birth - does he crawl back into her womb?!? The accelerated de-aging also makes no sense: people don't get older faster when they travel at high warp speeds in the "real" universe - why do they get so much younger in the reverse-universe? And why do only the people and their uniforms de-age, but not anything else like the Enterprise itself. These problems are sorta explained in Allan Dean Foster's novelization but even he has Spock and others comment on the silliness of these issues. Author Fred Bronson claimed this was due to Einstein relativity, but that clearly doesn't apply at warp speed. In "normal" space the crew doesn't age as rapidly as they deage when travelling at warp.