Fridge Brilliance: 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.
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 dragon ball (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?
Though the Kamehameha is stated to be an air technique in a metaphysical sense, it is still made of ki - which is pure spirit energy that can be manipulated to mimic or increase the power of a natural element. Though the Ki effects were nothing like the anime they looked like they were based on actual concepts of Ki. In basic science the only thing you need to fuel a natural fire is oxygen aka air, so Goku manipulated the oxygen and used his Ki as a spark for the oxygen to ignite. That being said Ki can also be manipulated into the other said elements above. Hence How Roshi was able to use the Kamhameha to defibrillate Goku. Not to mention in the animé Roshi used the wave to put out fire as well so causing a fire would be easier.
It should still be noted that Roshi using the Kamehame wave 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.