Visible crew/equipment: In the scene where Sulu flies the helicopter and accidentally turns on the windshield wiper, look closely at the bottom of the wiper and you can see the crewman's finger manually moving the wiper.
Continuity mistake: Gillian's Chevrolet pick-up truck is obviously two different trucks, depending on its location. When near the aquarium, the grille is a series of large, rectangular openings. But when at the park, where the Bird of Prey landed, the grille is a much tighter series of more numerous, smaller rectangles, made up of much thinner bars. This difference is consistent through the entire film.
Plot hole: When Spock analyzes the call of the probe and compares it in a phylum search, he's presumably interfacing with the Federation memory bank as mentioned in Sulu's pre-launch status. However, the alien probe was disrupting all power and communications in the vicinity of Earth. It's extremely unlikely the ship could've interfaced with the Federation memory bank at the time of that search.
Factual error: The "whaling boat" is too small to function as such. It isn't large enough to hold a fin, let alone disassemble a humpback whale.
Revealing mistake: When Chekhov falls on the aircraft carrier a cloud of dust flies up as if he's landed on a mat or soft cargo. When we see him on the floor it's concrete.
Continuity mistake: The Bird of Prey is the one captured by Kirk's crew in ST III That ship's bridge showed Klingon Cmdr Kruge in his elevated command chair with his helmsmen arrayed circularly below him, and nothing else. ST IV has this same ship, however the bridge now resembles The Enterprise layout with Kirk's command chair behind Sulu and Chekov at their rectangular helm, with Spock, Scotty and Uhura at their usual positions.
Other mistake: When we first see the Klingon bird of prey on Vulcan (just before we see closeups of the "Bounty" written on the side) it is clear that the ship is far too small to contain a pair of adult humpback whales plus 18000 cubic feet of water in its hold. Later, when the ship is hovering above the sea after foiling the whaling ship's attack it seems considerably larger.
Other mistake: During the inquiry at the start of the movie, the Klingon Ambassador is going over the footage of the destruction of the Enterprise from all the exterior views. This is very nice, but how would they have access to all of these different viewpoints of the destruction? Bearing in mind no-one was there to film it. It couldn't have been the Klingon Bird of Prey that filmed it, because in most of the destruction scenes, the Bird of Prey would have been no-where near or in a position to film it, and was of course captured and still being commanded by Kirk during the course of the inquiry.
Other mistake: When Kirk uses his hand phaser to melt the lock on the door in the hospital operating room, the phaser is not pointed directly at the lock. The beam leaves the phaser at an angle, which is probably not how the phaser would have been designed to operate.
Continuity mistake: Notice the candle on the table in the Italian restaurant scene during Capt. Kirk and Dr. Gillian dialog. It changes height depending who is talking.
Factual error: When Chekov and Uhura first see USS Enterprise and then later beam aboard, the carrier shown is not USS Enterprise (a nuclear aircraft carrier), but rather USS Ranger (a conventional or oil-fired carrier). The most obvious clue is the "island", the huge structure that sits on the deck of the carrier. USS Enterprise has the most distinctive and unique island of all the USN carriers, being totally cube-like in appearance. The carrier in Star Trek IV has a more conventional style island. [It is true that the USS Ranger was used in lieu of the USS Enterprise for the movie. This is because the Enterprise was on deployment at the time. Though by the time the movie was made the Enterprise had had its distinctive pagoda-like island rebuilt by Puget Sound Naval Shipyard in 1980, the aircraft carrier served until 2012 with a still-distinctive cube shaped island.]
Visible crew/equipment: During the scene on the bus, two members of the camera crew are visible in the window behind and to the right of Spock. The crewman of the left is sitting and operating the movie camera, and the crewman on the right is taking still camera shots.
Visible crew/equipment: During a close up of the police officer's sunglasses, when Chekhov is asking for directions to Alameda, some crew are visible in the left lens. They are a line of people trying to stay out of the camera.
Continuity mistake: When we first see the whale pen it is divided from the sea by a concert wall with double gate in the middle, but when the whales are released most of the wall and gates are missing.
Revealing mistake: When Kirk and crew flee the hospital McCoy bumps a man with his leg in a plaster cast. Look closely at the cast - it is fitted over his PJ's leg like a boot, plaster casts are never fitted over clothing.
Visible crew/equipment: At approximately 01:32:50 on the Blu-Ray, you can see a diver releasing the mechanical whales. He is on the far right side of the screen, you can make out his head, body and left hand. He is visible for a good 8-9 seconds. If you have a different media source, it's during the Bird of Prey decent. You see a closeup of Kirk, followed by a closeup of Uhura and Gillian, then a close up looking down on the harpoon. It's in the following scene.
Audio problem: When Gilliam slams on the brakes, the tires make a screeching sound, but the wheels come rolling to a stop, ergo do not skid.
Revealing mistake: When the whales first swim past the now submerged Klingon Bird of Prey, if you look to the right where the water is supposed to meet the distant horizon, you can see an exposed edge to the 'horizon' as the water moves up and down. This is the edge of the pool they are in, and the exposed edge is the bottom of the painting of the sky behind them.
Continuity mistake: In the second last scene when the bird of prey crash lands under the Golden Gate bridge, Kirk orders Spock to blow the hatch so the crew can escape. The camera is pointing up inside the ship to the outside of the ship and you can see the top of an industrial shed
Factual error: At two points in the film, the Klingon vessel Bounty traverses the distance from the Earth to the Sun at maximum speed, in excess of Warp 9. The latter sequence requires about 111 seconds from the time Sulu says "Aye sir, warp speed" until they reach the Sun. While there is no real science behind Star Trek's "warp technology, " the Starfleet Technical Manual provides a formula for calculating warp speed, whereby Warp 9 translates to about 136 MILLION MILES PER SECOND. The Earth is only 93 million miles from the Sun. In the apparent time that it takes the Bounty to reach the Sun, a starship traveling at such ferocious velocity would already be outside of our known solar system and deep into interstellar space.
Plot hole: If the Bird-of-Prey went to warp speed right after the whales were beamed up the ship would have already been so far away from Earth it would have been on its way back towards the sun, yet minutes later the ship is shown leaving the Earth, still at warp speed.
Factual error: They are about to perform major brain surgery on Chekov, but he is not nearly prepped for such a procedure. His head is not shaved, the area is not marked or masked and it has not been swabbed with Betadine, even though they are about to cut into his skull with a bonesaw. The "they haven't had time to prepare yet" argument doesn't hold water, because the surgeon is already approaching Chekov's head with the saw.
Continuity mistake: The crew wrote 'HMS Bounty' in large red letters on the side of the Klingon Bird of Prey, but in all subsequent flying shots, the large red writing is never seen again. It's not burned off as you only get heat entering the atmosphere if the speed is sufficient, and it's not wind resistance either, because the lettering is missing just after they take off.
Factual error: As they descend into the park, Uhura gives a bearing and range of 283 degrees, 15.2 kilometers to the whales, which are supposedly in a marine park in Sausalito. 283 degrees would put you in the Pacific Ocean, because Sausalito bears around 360 degrees from the park. Uhura gives a true bearing to the whales, since a relative bearing would be useless once the crew leaves the park.
Continuity mistake: In the operating room, when Kirk uses a phaser to melt the lock, the hand he is holding the phaser in switches hands in the closeup shot. Additionally, the arm holding the weapon in the closeup is no longer in hospital scrubs, but a similarly colored sweatshirt.
Continuity mistake: When the 'Bounty' materializes right above the whaling ship, it casts it into shadow. But the close-ups of the captain and navigator as they frantically turn the ship around reveal no trace of a deeper shadow on their faces and the surrounding waters; the lighting remains the same as in the scenes when they try to catch the whales.
Continuity mistake: In the scene where Kirk and Spock are walking down the street after Spock has been in the tank with the whales it is clear that it is a windy day. Both of them have their hair blowing in the wind and yet as they are offered a ride in the truck and the shot leaves them for a moment their hair is suddenly fixed again.