At 20:13 and 21:57, Sulu can be seen on the bridge of the Enterprise while he's still on the planet. He suddenly replaces the man (crewman Gabler?) filling in at his station when the angle changes. Crewman Gabler, while appearing on the bridge, simultaneously joins Scott in trying to enter the Computer Bay.
At 2:33 as Uhura lounges by the water, her reflection misses both rank stripes and the familiar "arrowhead" insignia on her uniform. All the trees behind her are missing from the water's reflection as well.
There are a number of changed premises between Shore Leave (1966) and this animated sequel. In "Shore Leave" the Keeper was not the last of his race (nor is he here). He only mentioned that he didn't think the Federation was ready to meet the others of his kind. The planet was not made for outside space travelers but for the Keeper's race to use.
At 16:45 the bridge contains only Scott, M'Ress and crewman Gabler. An alarm sounds. The artificial gravity is gone. Now there are five people floating in the bridge, suddenly including Lt. Arex and an unnamed crewman in a blue shirt.
From 7:37 onward, M'Ress is drawn wrong, with an entirely black nose instead of just around her nostrils.
Unsupported by gravity, Scott pries open a hatch to Engineering. Shown floating in mid air, he has no weight or physical support to put toward opening the hatch. His effort should, instead, have shoved him gently aside into the wall.
When the shuttlecraft bay begins to open, the doors are mistakenly shown as one large door opening from left to right. The bay actually has two doors that open in the center and retract into both sides.
For two seconds, the harnesses on Arex and Sulu "jump" off their bodies. Evidently an animation plate slipped out of alignment during the shot. It's an additionally curious scene as Mr. Sulu is still on the planet fighting alongside Dr. McCoy.
At 21:17, Spock talks to the planet computer. He's in close-up, but his mouth isn't moving.
Seen from within, the giant cat reaches into the cave, but lines of the cave entrance overlap the cat's paw as if it's still entirely outside the cave, but in the immediate next shot, it just misses snagging Mr. Spock.
At 10:20, Uruha's head looks particularly flat, as if a cardboard cut-out.
With the planet trying to kill them, the landing party draws a wild, illogical conclusion that the planet's medical protocols operate separately and independently, treating all who might get hurt.
McCoy injects Spock with Melenex, which induces unconsciousness and skin discoloration that looks worse than it is. As proved in By Any Other Name (1968), Spock can self-induce a state mimicking near death. That would negate the need for Melenex except for its skin discoloration property, which is barely noticeable.
To escape a winged, fire-breathing dragon, Sulu thinks he and McCoy should scale up a mountainside (where a flying dragon would have an easier time picking them off).
Sulu thinks the planet's triangular hovercraft looks like a mechanical nursemaid. How does he come up with THAT idea? And why does he risk the landing party's detection by voicing this needless opinion aloud?
Once the hatch is opened, Mr. Scott propels himself forward, apparently under his own, inherent gravitational power that makes humans such naturals for space travel.
Spock says the Queen of Hearts appears in Lewis Carroll's "Alice Through the Looking Glass". She actually appears in Alice's Adventures in Wonderland, and the correct title of that book's sequel is "Through the Looking-Glass, and What Alice Found There".
Kirk beams down, putting Lt. Arex in charge, but Arex stays in his seat at the navigational controls rather than move into the captain's chair as others have done.
Uhura's high-pitched mosquito-like nose singing does not match the beauty of her singing heard in Star Trek (1966).