How does the Enterprise get to the galactic core in "The Magicks of Megas-Tu"?
The same way they get to the galactic core in Star Trek V.
In "The Lorelei Signal", Kirk, McCoy, and Spock are all aging at the same increased rate. Spock says that the rate is ten years a day, and they all grow super-old together. But Vulcans live for a little over 200 years, and McCoy is older than Kirk anyways. How are they all the same age?
Spock does say that he will retain his strength longer than the others, for that reason. But yeah, he gets just as wrinkly as they do.
Supposedly this is the draining of life force, not actual physiological aging. So you drop from 100% to 0% at the same rate. Except, of course, that Spock doesn't. The short answer, I guess, is that it's a mistake to expect realistic geriatric portrayals in a situation where Space Patrolmen are having their mojo drained by vampire space vixens. MST3K Mantra ahoy!
It isn't clear exactly how history got fouled up in "Yesteryear." It apparently has something to do with the impossibility of Spock being in two places at once, but then the problem ends up getting fixed by Spock being in two places at once.
The part that I've never really grasped is this. Kirk and Spock are off in exploring "Orion, at the dawn of its civilization." The implication is that everything goes wrong because there are two versions of adult Spock in the past. Now, since this has never kicked in any of the other times Spock has time travelled, it must be because both Spocks are present at the same time. But the dawn of Orion's civilization sounds like it's in the distant past, whereas he events on Vulcan would have just taken place a few decades earlier.
IIRC, the issue was caused by the researchers viewing a period of Vulcan history that Spock was supposed to be present for, but was instead in Orion. Since he was elsewhen, he wasn't able to be there to effect the changes that he needed to, so the timeline got frakked.
Apparently, it's colorblind Hal Sutherland's fault that a lot of things in the series that ought to not be pink are, not to mention the white Andorian (decades before the Aenar would be invented, though Thelin's been one in the Expanded Universe since their introduction) or the Orions being the color the Andorians should be instead of the usual deep green (as in Green-Skinned Space Babe.) So one obvious question needs asking: Why, why, why did they let a colorblind guy have any control whatsoever over the art department? While it's harsh, someone at some point should have said as tactfully as possible, "Sorry, Hal, but you just don't have 'green.'"
Is it not the case that Sutherland did not realize he was colourblind till later? However, I take that the point that if nobody ever said, "Hey, your colours are awfully weird, what's the deal with that?", it must be the case that quality control on TAS was weak indeed... but that's hardly surprising by looking at the finished product.
Under influence from a Love Potion in "Mudd's Passion", Spock not only declares eternal romantic devotion to Christine Chapel, he also begins being palsy-walsy with Kirk. We know he likes Kirk, but he seems to have no romantic interest in Christine normally. Can the potion simultaneously add new relationships and pump up the old ones?
The potion is specifically stated to cause love in the first person touched. The rest is side effects.