The painted-on "HMS Bounty" on the Bird-of-Prey is visible only when Kirk asks his crew if they will stand trial with him.
Right after the Bounty has landed in the park and the trash men start to flee, some of the trash cans nearest the truck are full to or nearly to the tops. But as the truck drives off, those cans appear to be empty.
The boat shown in the movie is too small to be used in whaling. It is a fishing trawler with a harpoon attached.
The hand that Kirk uses switches when he melts the lock during the rescue of Chekov from the OR.
When Dr. Taylor drops off Spock at the park, the ignition switch of the Chevy pickup is shown in the "off" position, yet engine idling sound continues and there is no sound of the engine starting up again.
Ships in the opening sequence that are affected by the probe lose power and come to an almost complete stop. In the vacuum of space, air friction does not exist, so they should keep going the same speed they were before.
When Kirk and his crew walk by San Francisco, Kirk looks a newspaper's 25-cent box where can be seen an issue of San Francisco Register, with the headline "Nuclear Arms Talks Stalled". Although not completely visible, time-date under the headline is marked as "Thursday, December 24, 1986". December 24 was Wednesday, not Thursday.
The Bounty's bridge looks very different than it did in Star Trek III: The Search for Spock (1984). It's possible that the Vulcan engineers working on the ship renovated it.
When Spock nerve pinches the punk on the bus, his music appears to stop even though no one actually turns it off. However, it can be presumed that the punk's head hits the 'off' switch.
The whalers speak Finnish, but they are in the Bering Sea, part of the north Pacific Ocean. As Finland has not commercially hunted whales in well over a century, the Finns may be mercenaries for Japan, which was still involved in commercial whaling in 1986.
When Spock is being tested by the computer, some camera angles are shot through the display screens. The text when viewed from the back is still displayed forward, which can be explained as a feature of a holographic alien device from the future rather than a goof.
The antique eye glass frames that Kirk sells to the antiques dealer when they first arrive in San Francisco are described as 18th century, but the frames have plastic temple tips and bridge pieces.
They could have been augmented or customized in the 500 years since they were first crafted.
They could have been augmented or customized in the 500 years since they were first crafted.
When the cloaked ship lands on the grass, a trash can is crushed. As the earth moves down under the pressure of the heavy ship, the grass blades remain pointing up.
During landing of the ship, garbage cans are "blown over" into the prevailing wind, and can be seen being kicked over by garbage man.
When Gillian is touching the cloaked ship at the park, there is a shot from above that reveals her right foot steps under the matted shot of the ship's print on the grass.
When Kirk takes Gillian's arm to take her toward the back of the ship to the whale tanks, he walks her directly into the door jamb. She hits it, recovers, and continues.
When the elderly lady is being pushed in a wheelchair, happily saying, "The doctor gave me a pill and I grew a new kidney", the nurse on the left side of the screen almost trips over the wheelchair, but manages to recover.
When Scotty is typing on the computer in the plexiglass factory and his hands are shown, the sound effects of typing do not match up with his hands, which are moving much slower. In addition, there is no way a single keystroke as demonstrated by Scotty could create the level of graphics shown on the 1986-vintage Macintosh computer used in the scene.
When Spock tells Gillian that Gracie is pregnant, she brakes the truck and we hear a squealing sound indicating that the tires have locked-up and are skidding on the road. However, the scene immediately cuts to a side shot of the truck stopping and the wheels are not locked - the truck comes to a gentle stop.
When Sulu accidentally turns on the windshield wipers of the helicopter, the wipers were broken so a grip had to move the wipers manually. Look closely and you can see his finger holding on to the blade as it moves back and forth.
Just before Spock checks the bus map at a stop, you can see several crew members are visible through a large glass window of a restaurant - one of them even clearly wears a "Star Trek IV" security badge, and all are wearing walkie-talkies.
When Kirk and Spock are riding the Muni bus, a crew member with a camera is reflected in the window behind them.
When the tour group is viewing the whales from above and it it sprays water from it's blow hole there is a small amount of smoke (you can tell the difference from water spray by the way it drifts out) that trails out after the initial spray possibly from the charge used to propel the water from the prop whale blow hole.
Kirk and Spock are seen walking as Dr. Taylor drives up. She asks where they are going, Kirk replies "Back to San Francisco." The scene is shot in the Marina District of San Francisco. Kirk and Spock are already in San Francisco, Sausalito is on the other side of the Golden Gate Bridge which is behind them. While it is possible that Kirk may simply made a mistake being from the future, Dr. Taylor later even mocks him at dinner saying that they couldn't even get back to San Francisco without a lift.
When Kirk and the crew first exit the ship after landing in Golden Gate Park, Uhura says the whales are on a heading of 283 degrees (Spock repeats this heading at the bus stop). 283 degrees from Golden Gate Park heads straight out to sea without passing near Sausalito.
After they all escape, Chekov's phaser is still in the possession of the military agents that had originally arrested him. While McCoy earlier in the film airs his concern to Scotty about leaving advanced technology (Plexiglas scene) or information of same in the past, no concern is given to Chekov's phaser, which is left behind. But then again it didn't work so it might be difficult to reverse engineer.
After the President gives his warning, Kirk gets up to talk to Spock.
When McCoy tries to discuss the afterlife with Spock, Spock states that they can't because there is no point of reference. McCoy then complains "So I have to die in order to discuss death?" McCoy did, in fact, die and then get "repaired" by alien technology in Shore Leave (1966).
After the probe leaves and the crew are celebrating in the water, Spock can be seen smiling, almost even laughing at one point.