Right. And the reason for that was that Roddenberry didn’t want to be tied down to what Earth would be like in the 23rd century, not that the Enterprise wasn’t allowed back. When they did go back in “Tomorrow is Yesterday” (though to the wrong century) no one said we shouldn’t be here.
They went back to Earth in that episode because of an accident (they’d almost collided with a “black dwarf star”). They went back on purpose in “Assignment: Earth” to conduct “historical research” covertly.
In TMoST, it says the Enterprise is “Assigned to a far-off sector of the galaxy” and “Except under orders from a higher authority, the Enterprise never leaves its assigned area.”
Excuse me… what does God want with a spaceship…?
the answer to that is found in chapter 29 of The Restaurant at the End of the Universe
A higher authority, not THE Higher Authority. Yeesh! 
I prefer Wink of an I, Mudd’s Womenageriena.
I thought we’d previously established that Bones actually died when the lance was driven through his chest and the Bones that appeared at the end of the episode was a replica created by the Caretaker.
If you look carefully in future episodes, you’ll notice that Bones always walks out of step with Kirk and Spock. 
Being halloween and all, I watched Catspaw for the first time in decades last night.
I never noticed that it has the same plot as The Rocky Horror Picture Show.
To wit:
Aliens come to our area, ostensibly on a fact finding mission, but get sidetracked when one discovers the joys of sensual pleasures. Thery abandon their primary mission to pursue these. They wear elaborate, inappropriate for the times outfits.
They kidnap some innocent travellers as part of their “festivities”. One attempts to seduce the travelers with sex (touch me). They offer unlimited power and knowledge (don’t dream it - be it!)
Eventually the true leader reasserts command and stops the proceedings, as they have failed their mission. One is killed.
The ending is a little bit different though. No one flies back home in the castle. Kirk doesn’t develop a fondness for fishnet and garters (we assume).
Huh. So TJ Hooker was about something other than what I’d been assuming, I guess.
If it had the comma, then maybe. “TJ, Hooker.” Like “Magnum, PI”
Except in the beginning of Tomorrow is Yesterday they thought they were in their present. And it didn’t seem to be an issue, though I think they said they were not that far away when the accident happened.
Sure they couldn’t go just anywhere in the Galaxy, but Earth didn’t seem to be special, and I could see Earth being a part of many patrol areas.
The math is kind of difficult. Based on the premise that we are in a galactic goldilocks zone (where stellar metallicity is high enough to generate life), at a steady TOS warp 8, it looks to me as though it would take a couple centuries to get to the other side of the galaxy (about 11Kp out from the core, meaning about 34Kp to the galactic antipode, if you follow a circle path).
Oddly, the edge of the galaxy, with its nearly impassible barrier (Where No Man has Gone Before, By Any Other Name, and, sorta, Is There in Truth No Beauty?), lies some 6Kp out, which means that warp 8 would still take you several decades to get there.
Five year mission? Yeah, I think not.
I had a flash of insight that they went ^UP to get to the galactic barrier. I mean, if it supposed to surround the entire galaxy, the sophisticated beings that made it must not be bound by “2 dimensional thinking.” (It just looks like a band because it fades out when it is off the narrow visual axis.*)
It’s only like 1000 lt yrs (more or less) straight up until you are “out” of the galaxy. A heck of a lot closer sthan 26K light years → thataway.
*either that, or it is an incredibly stupid mistake. Early starships less sophisticated than the Enterprise went 26K light years? Yeah, right.
Put it down to early installment weirdness. * They hadn’t quite worked out yet how fast or far the ship could travel.
*Beware: TVTropes link.
I like Spock’s Brain and the one with the Yangs and Coams. I hate the one with the Space Hippies and Turnabout Intruder.
When I was a kid Star Trek pretty much aired every Saturday and Sunday at 6pm up until it got booted out of the slots for TNG. Still I somehow never managed to see Space Seed until well after Wrath of Khan was readily available to see via cable or home video.
No, ST was always thin on the ground with stuff making sense. They had some breathtaking errors that simply could not be put down as the magic of technology surpassing contemporary understanding. If you want real science that is consistent and makes sense (to the extent that it can), I recommend Futurama.
Like the OP @kaylasdad99, I have also been slowly chugging through the ST:TOS on Netflix, reliving my teen “trekkie” years. As I noted in a previous post the series is not nearly what I remembered it to be and I find most of it badly written and cringe-worthy.
I just made it to the final episode of S2: Assignment Earth. I recalled the episode and Gary Seven as a character but I was absolutely blown away at the start of the episode when Kirk casually tosses out that using the “light-speed breakaway factor” they’ve traveled back in time to observe 20th century earth.
Stop the clock! Did I hear that right??? WTF?!?!?! You’ve mastered time travel?!?!?!
I don’t think teenage me watching after school ever quite picked up on that intro or thought about the implications, but f-me, that changes everything!!
Sure, they first traveled through time in the season 1 episode Tomorrow is Yesterday, when they were drawn towards a black hole. They used warp power to break free, but the slingshot effect sent them to the 20th century. That first time was an accident, but they successfully returned to the 23rd century by flying toward the sun and using its gravity as a slingshot.
They repeated the effect to return to the 20th century in Assignment: Earth and again in the movie Star Trek IV: The Voyage Home.
Yep and the show has suffered for it ever since.
Whether you believe they time travel too much, or not enough, they just don’t use the tech to its inevitable conclusion.
They never use ANY tech to its inevitable conclusion.