At first, Roshi says that Goku isn't powerful enough to defeat Piccolo and Oozaru. Suddenly, in the last battle he is strong enough. Why? Because Saiyans get a power boost after they recover from being near death, and that's exactly what happened to Goku in the previous scene.
Ki attacks being referred to as airbending sounds slightly less stupid if you remember that one of the ways to properly harness ki (or chi, in the Chinese vernacular) is proper breathing. Heck, chi literally means breath.
Also, as mentioned on the main page, ki attacks are Invisible to Normals, so from the perspective of those who can't use them they appear to consist of moving air.
The Oozarus could have been two different Saiyans. The first disappeared (read: returned to human form) when Piccolo's controlling power waned; Goku was merely the newest handy Saiyan.
If Bulma thought that there was only one dragonball (the "prometheum orb"), and expected it to stay safely in a museum, then why did she make a dragon radar?
It was never in a museum, it was being studied. She made the radar to find it after it had been stolen.
If the Kamehameha is an air technique, how can you use it to light torches?
It should still be noted that Roshi using the Kamehameha to extinguish the fire in Ox Mountain was a last resort method; they originally had to lend a feather from Roshi, that was said to blow a powerful wind. Roshi ended up putting the fire off because he disintegrated the whole mountain along with the fire; The Kamehame attack EXPLODES on contact versus everything. A minor consideration: pressurized air can explode in flames since the molecules in the air move faster; it's based on this principle that the combustion engine can work; the fact an electrical spark is used to ignite the air-combustible mix is only to RELIABLY make it explode on a timed schedule; if not enough oxygen is present, even the spark can't ignite the combustible mix, hence, your car's engine can stall sometimes.
In the end, why the hell didn't Goku wish everyone was resurrected? He wanted to resurrect Master Roshi, but he (as well as Goku's own grandpa in this film) fell under the "everyone" blanket (and were all dead recently enough to count).
While this is explained in the source material Grandpa Gohan didn't want to be wished back to life, the movie doesn't justify this. And the funny thing is, if they had just added one line to the scene where Goku is in a state between life and death, and sees his Grandpa again, they could have avoided thisnote Just have Granpda Gohan say "My time has passed" or something along those lines.
Why, when Bulma came into a random destroyed house, was her first instinct to point a gun at the first person she saw?
Anyone would have done the same until they learn the truth and the gun or any weapons in general will be lowered.
It wasn't a random destroyed house, she had followed her radar, which told her the dragonball was there. Since she didn't know there were multiple balls, she thought whoever had the ball in the house was the person who stole hers. Because she thought the ball in the house was her ball.
When Kakanot first sees Bulma, he asks if she's Piccolo, despite the fact that Grandpa Gohan clearly stated Piccolo is a he.
A stranger shows up in his house after it's been destroyed, obviously looking for something? It's possible Goku assumed Piccolo was a shapeshifter and had returned to double check the ruins.
