Other mistake: Fuller's car "explodes" collapsing for no reason, it has been hit with a couple lead pipe swings by a creepily old teenager, never by Goku. And if Goku did it with his Ki, then he'd already have mad power levels, contradicting the rest of the movie. Even throwaway jokes (I would imagine this was supposed to be one) should at least attempt to make sense, or "not not make sense." (00:17:05)
Other mistake: When Goku meets Bulma for the first time, he asks her "Are you Piccolo?" Gohan said that "he's returned", and since Goku knows the whole story about Nameccians, he obviously also heard the story about Piccolo tons of times. There's no possible reason why he'd mistake a girl with a gun for the powerful male-looking sorcerer mentioned by his grandfather (it'd be also pretty surprising if his Grandpa talked to him about the alien race thing but neglected to mention that they are green-skinned and distinctly non-human looking). (00:23:45)
Other mistake: Once Goku has punched Mai in the face, his friend joins him and there's a shot of the monster corpses in the lava shifting and being swallowed by the incandescent substance. In the green screen background conversation with Muten though, the corpses are still there, completely unmoving - not that it made any sense to begin with that they'd stay put, indestructible, forever. (00:46:35)
Other mistake: Goku turns into Oozaru, and his uniform opens up. Goku reverts to his normal self.and he is also nicely tied back up, sash back in its place, undershirt, etc. Instantly. (01:06:00 - 01:09:00)
Other mistake: Piccolo kills Gohan using a Vader-esque power to choke the opponent, and crushes the wooden part of his house on top of him (a very large part, some mistake it with the whole house) with a display of great telekinesis that takes him seemingly no effort. Throughout the movie, he never shows this kind of power and control over objects or people ever again.
Other mistake: The history in the world of this movie does not have to follow our own (after all, in Toriyama's creations we have dinosaurs roaming the Earth, and talking animals), however the opening narration talks about how "thousands of years ago" Piccolo bringing our "peaceful planet" and "the HUMAN RACE, on the BRINK OF ANNIHILATION." The movie is set in 2010-ish (Goku has a poster of the "Pazu United" football team, year 2010), and turns out from later dialogue that Piccolo is coming back after 2,000 years. The implausibility of a nearly world-ending global catastrophe happening barely 2,000 years ago and being completely erased from history (nobody remembers Piccolo and everybody laughs off the notion of an invasion around that time) is astonishing, but even admitting that, the opening crawl briefly shows warriors in full plate armor, definitely out of place for circa the first century AD. Everything about the narration leads to a very far back mythical pre-historic past, so when later it turns out it's" just" 2,000 years ago, it makes no sense.