7. King Kai is a huge asshole
King Kai is kind of like the Yoda for Dragon Ball Z, unassuming but exceedingly wise. He helped Goku learn powerful techniques like the Spirit Bomb and Kaio-ken, and continued to provide sound advice throughout the series via telepathy. Though King Kai is about 80% Solid Dude, the other 20% is a real piece of shit. This goes beyond cracking inappropriate jokes and giggling while his students chase a monkey around his planet -- King Kai's arrogance has cost lives.
It all comes down to one moment late in the series, when Goku is trying to find the planet of New Namek so that he might bring back a new Guardian of the Earth. While Goku does have the power of teleportation via Instant Transmission, he doesn't know New Namek's location. King Kai agrees to help, while at the same time learning of Goku's knowledge of IT. Cue Kai quickly trying to cover for himself.
So this whole time, King Kai knew about Instant Transmission, but just never bothered sharing with Goku. Kai's explanation? The ol' "You never asked!" excuse. As though Goku would have had the foresight to ask whether there was a way to magically transfer his physical body from one point in space to another. The flimsiness of that excuse is magnified by the fact that Goku never "asked" to learn about a technique that could gather the energy of living things into one massive sphere, but King Kai taught him about it anyway. Dude is supposedly the "Ruler of the North Galaxy," and he couldn't even be bothered to teach arguably the most useful nonviolent move in the known universe.
But at least Goku learns it eventually, right? It's not like he could have used it at any point before th-- OH WAIT
Remember, Goku not only had to travel 10,000 miles down Snake Way to get to King Kai's place -- he also had to travel down the same path on the way back after being wished to life. Thanks to his intense training, it only takes one day for Goku's return trip down Snake Way. But in that time, Vegeta and Nappa arrived and decimated the Z-fighters.
You know what would have helped in this scenario? Instant fucking Transmission. If King Kai had told Goku about the technique beforehand, Goku would have made it back with plenty of time to save his friends. Instead, Piccolo, Tien, Chiaotzu paid the price. As for Yamcha, well, there was probably no helping that.
It's not clear what's worse -- that King Kai knowingly withheld the info regarding Instant Transmission, or he completely spaced that possibility during a time where it would be most useful. Either Kai is an arrogant dickweed or an ignorant asshole. Maybe both.
6. Piccolo blowing up the moon would have messed up the planet
Even though Piccolo is kind of stuck on the B-team for most of DBZ, he's still super-important to the series in a lot of ways. One of the most notable arcs for Piccolo came when he took young Gohan under his wing after Goku had that uh, unfortunate run-in with Raditz. Piccolo put it on himself to train Gohan in preparation for the Saiyan invasion; his parenting technique was a little rough, but it was tough love.
Now, it's hard enough taking care of a five-year-old as it is, but imagining babysitting a kid who wolfs-out into a giant monster at the sight of the moon.
When Gohan makes his first transformation into Great Ape form, he and Piccolo are roughing it in the barren plains that seem to cover most of the Earth in DBZ. Though this kept immediate casualties to a minimum, there'd be a real problem if Gohanzilla managed to make it to civilization.
Piccolo had to think quickly. On a whim, he surmised that the big shiny ball in the night sky was the culprit for Gohan's transformation, and so Piccolo took care of it. In other words, Piccolo blew up the moon.
Wow, that's impressive. Piccolo didn't even have to use his special beam cannon or anything, and that moon was toast. Gohan turned back into his human form, but there's still a problem. There are now HUGE CHUNKS OF MOON hurtling towards the Earth. This is the same sort of problem facing the surface of Endor after the second Death Star explodes at the end of Return of the Jedi.
Star Wars managed to explain away the Endor problem by asspulling something about a malfunctioning warp drive teleporting all of the debris to a distant plot hole far, far away. But in DBZ's case, that's no space station -- it's a moon. Meaning that much debris has nothing to do but rain down down on the surface of the Earth, pulverizing the crust and destroying much of the planet.
We could be generous and say that Piccolo, champ that he is, zapped every hunk of moon that didn't burn up in the atmosphere. That wouldn't even matter. The earth is STILL fucked because it has no moon. It's sort of the reverse of what happened at the end of the Fifth Element. Without the moon's gravity, the tides would be greatly diminished. You could also say goodbye to the Earth's tilt, which means no more seasons. The moon is even responsible for slowing the rotation of the planet -- without that gravity, our days would be about six hours long. Not only would that mess up all sorts of plant and animal life (and your work punchcard would be screwed), the sheer speed of the planet spinning would whip up intense and constant storms. Even though Piccolo thought he was doing the right thing, he essentially messed up the Earth permanently to avert a temporary disaster.
The worst part? Master Roshi already ran into this same problem with young Goku during the Z-less Dragon Ball. Roshi's solution: To blow up the moon. The exact same moon.
At some point in Dragon Ball, it's explained that Kami magically reconstitutes the moon. We can assume that's also what happened in Dragon Ball Z, since the moon shows up once more about a hundred episodes after Piccolo's incident. That still leaves years for the Earth to have no moon, which would have irrevocably damaged life and civilization all over the planet. Almost as bad as say, a supervillain showing up every six months.