Corrected entry: At the beginning of the movie, the Excelsior is hit by a shockwave coming from the Klingon moon Praxis (the Excelsior would be in Federation space, dozens of light years from the moon). The force of the shockwave is such that the ship is physically thrown about, as are the crew. A blast that is so strong at such an extreme range would surely destroy not only the moon but also the Klingon homeworld and most other things in Klingon territory. This, however, isn't the case; Praxis is later shown to be only half destroyed.
Corrected entry: Captain Kirk and Dr. Mccoy escape from the Dilithium mines together with the shape shifter. They go to the surface and get out of the magnetic shield that prevents Enterprise from beaming them up. When they fight and get discovered later, it seems it is all a setup and they are beamed up by Enterprise just before they are shot. But why did the shapeshifter lead them to a place outside the magnetic field? If only they were inside it (no markings around to show they are outside the field), they could never have been saved.
Correction: The Klingons (for whom the shapeshifter is working), need a reason to shoot/kill Kirk and McCoy. I know, I know, Klingons don't normally need a reason to kill something, but this is a special case. Kirk and McCoy weren't killed after their trial as a peace gesture to the Federation. Killing them inside the shield, from which they can not be rescued, would be seen by the Federation the same as executing them. By them being outside the field, where they can escape, they are fair game to any prison warden. The Federation would understand that their death was acceptable under the circumstances and the summit on Khitomer would continue as scheduled, giving the conspirators a chance to kill the Federation president, just as they killed the Klingon Chancellor. They've been trying to start a war the whole movie, but Kirk keeps getting in the way, by trying to save Gorkon, by actually escaping from Rura Penthe, and then by disrupting their attempt on the President. Without actions of the crew, the conspirators would have succeeded.
Corrected entry: When Spock mind melds with Valeris, you hear a heartbeat. Whose heartbeat is this? It is specifically stated in the original series that Vulcan hearts beat almost twice as fast as humans. It is, however, never established that Vulcan metabolic functions slow during a mind meld, due to conscious physical control or otherwise.
Correction: It was "never established that Vulcan metabolic functions slow during a mind meld." Not "it was established that they do not." If something is not established one way or the other, then there is no contradiction and therefore no error.
Correction: The heartbeat is almost certainly not diegetic.
Corrected entry: The character of Valeris was originally slated to be Lt. Saavik. The filmmakers tried to get Kirstie Alley back, but found out that her stardom in "Cheers" now made her too expensive. It was then decided that Saavik as she was known would never betray the Federation, so Valeris was created. This explains Valeris' infatuation with whether Spock is lying, as her words were originally Saavik's, mirrored in "The Wrath of Khan" (when Spock tells her, "I exaggerated," after she accuses him, "You lied.").
Correction: First, Saavik was already recast with Robin Curtis for Star Trek III and IV, so Alley was barely an issue for this film. Second, the exchange you mention is not a reference to the earlier film, but to the long-standing stipulation that Vulcans, as a rule, do not lie, established early in the original 1960s TV series.
There's nothing incorrect about the entry. Valeris was indeed originally written to be Saavik and Nicholas Meyer did try to get Kirstie Alley back (he did not care for Robin Curtis' interpretation of the character). The dialogue about Spock's apparent lies works with Valeris, too, but as originally written they would have been references to their earlier conversation in Star Trek II: The Wrath of Khan.
Correction: This is actually quite easily explained. There are three components to consider, the nature of the shockwave, the direction of travel, and the relative masses of the Excelsior versus star systems and planets. The shockwave we saw, first of all, was subspace-based. This accounts for how fast and how far the shockwave travelled. The accident was caused in a dilithium mining facility, an explosion of any type surrounded by that much dilithium would necessarily cause a strong subspace reaction. Next, an explosion does not necessarily always explode in all directions evenly. When a reactor wall gives way, the explosion goes in all directions, but it does NOT DO SO EVENLY. The bulk of the force goes where it is easiest for it to do so. Were this not a fact of physics, rocket engines would not work. It is not at all inconceivable that the primary force of the explosion was outward away from the planet, and only enough force went in the other direction to shatter about half the moon, thus sparing the other half of the moon and leaving Kronos initially untouched physically (though radiation dammage and the falling debris will soon cause major trouble). Now, even with the shockwave travelling out away from Kronos, everything along the way is going to be hit. But the amount of force in the subspace shockwave shown in the movie CAN NOT POSSIBLY equal the force of the PHYSICAL shockwave. The subspace shockwave was created from translating part of the energy of the physical shockwave into subspace. Also, the original author seems to use laws of physics that apply to the physical world when guessing the power of the initial shockwave. However, subspace is a VERY energetic medium, so while some power would be lost, a subspace shockwave would last much longer (time) than a phsical shockwave, because it would lose power much slower. So while the Excelsior was tossed around like a poker chip, a planet with a mass BILLIONS of times that of the Excelsior (much less a star with an additional few million or so times as much mass) would be completely unaffected.