I always found "The Galileo Seven" to be one of STAR TREK's finest adventures.
Quite a bit has been made in this thread of a few issues...
The shuttlecraft crew giving Spock a hard time, Kirk giving Ferris a hard time. Did each go over the line? Let's take Kirk first. Kirk, in the TOS era, is a starship captain. In the TREK Universe, that sets him apart. He's a special kind of commander, not unlike an outpost commander. He takes his ship out on the frontier where there are no friendlies or communications with home for considerable periods of time. That means he's not just responsible for his ship and he's not just the Federation's point-man "out there", he also has to be largely autonomous. He's "it", and Starfleet better make sure they promote the right officer to sit in that "center seat". So when Kirk makes his "nose off my bridge" remark to Ferris, it is an eyebrow-raiser, but Ferris seems to expect the insolence. After all, this is Kirk's bridge and this ship goes into frontiers and hazards the home crowd wouldn't touch with a ten-foot pole. What is surprising is McCoy's remark about this shuttlecraft ride being Spock's "first command". In a sense, the Murasaki-Galileo mission is like mini-starship mission. Spock is placed in command, and that makes him God. But he's a full commander, and he never commanded a shuttlecraft on a hazardous mission before? That doesn't seem right.
The whole point of this story was to take the proud, "in control" officers on the Galileo and temporarily maroon them on Gilligan's Island long enough for the civilized veneer to slip away and get them bickering at each other. Even Scott chides Spock about "a phaser can only drain so fast". It's a survival situation, and Spock is too busy being a Vulcan professor. It is entertaining to watch, even though it would've been outright hilarious if none of the characters had been needlessly killed. Despite the "Dreadnought" suggestion that Boma had been given the boot, I would expect no action was taken. If an inquiry were initiated, Spock's competence would be the first thing under review. Given Spock's poor handling of the "natives" (a few phaser shots might've changed everything) if anyone were to be punished the punishment would start at the top. Boma and McCoy can easily be forgiven on this one.
One minor point, maybe making a mountain out of a mole hill, would be Boma's remark just before the shuttle first looses control in space. Note that he pipes up "That's to be expected, Mr. Spock." Let's not dismiss Boma's role in the original mission plan. Spock may have been in command, but the mission wasn't (originally, anyway) all about him. It could be that Boma was expecting to be every bit as much "Mr. Murasaki" as Spock, and he was just sounding off as a professional at that point. We see this again just after the crash (when Boma was cleaning his nose) and he can't stop chatting about what he thought about what happened. That's part of the core of this episode: the characters knew there would be danger, but were still surprised when they were thrust into it, and then they discover they're in over their heads and the civility evaporates as they fight to survive.
Uhura, the multi-purpose wonder. Some comments have been made about Uhura stepping up to report to Kirk on findings. Was this appropriate, or was it out-of-character? There are a couple of issues to consider. In the military, officers are generalists. NCOs and Warrant Officers are specialists. While it is understandable that there would be quite a bit of specialization on a starship bridge, it should be pointed out that Uhura running Spock's science station in a pinch seems no more radical than Chekov's subbing for Spock when Spock is away, or Uhura at the navigator's station, or Scott at the helm, or Spock making a medical diagnosis on the surface of Argus X...
Uhura's regular job is to be chief of communications. Despite the poor job the writers and producers put forth of using her character as an important part of the bridge crew, her in-a-pinch service in "The Galileo Seven" seems to be just what the doctor ordered. With the Murasaki ionization ruining all external communications, what else is Uhura going to do? Sit there and read static? As a junior officer in a position of department head, and naturally as a generalist, she should be expected to step up and take the initiative. BTW, this isn't the only time she does this. Check out "Whom Gods Destroy" and "Spock's Brain", if memory serves.
Back to the O.P.: Should the shuttlecraft have been launched in the first place? Well, this is a Federation starship we're talking about. She is a frontier vessel and Kirk has standing orders to investigate phenomena like the Murasaki 312 Effect. This isn't just some random order that Starfleet hands down. Given the dangerous situation the shuttlecraft mission becomes, it seems quite logical no only that Starfleet would give such an order, but also that command-grade officers like Kirk and Spock would be eager to jump in with both feet. They're like moths drawn to a light, with this one. It's their nature.
There are other issues about this ep I could nit-pick about. Why are the Galileo crew in their everyday duty uniforms during a shuttlecraft mission? Shouldn't they be wearing work jumpsuits for flight? This is actually a significant issue for me. Every time they take a shuttlecraft into deep space, they should be wearing a flight uniform. This would only seem appropriate. It would have the effect of eliminating the silly Mears-in-a-mini deal right away.
And if heavy interference is blocking transporter functions, would you step into one of those machines? I have to wonder what landing parties on foot were supposed to accomplish when scanning an entire planet.
If "The Galileo Seven" had been made in the last 20 years instead of 44 years ago, what do you think of the likelihood that Taurus II would be inhabited by dinosaurs instead of King Kong?