The one big mistake
a lot of science-fiction of the 20th century made was the idea that we would or could perfect any kind of anti-gravity in the near future.
All the devices we thought would become commonplace in the new millennium - personal jetpacks, flying cars, hoverboards, the floating camera drones in Babylon 5 - are all predicated on the idea of flying with very little expenditure of energy.
Earth's gravity at the surface pulls us downwards with a constant acceleration equivalent to a car doing 0-100 kph (0-60 mph) in 2.8 seconds. Only the most powerful high-end sports cars can achieve anything approaching that. Any device intended to fly must effectively match that acceleration upward merely to hover, let alone gain altitude. And it must maintain that acceleration even when put under load - such as a human being riding the thing. However you colour it, it takes a lot of energy to impart that kind of acceleration to anything much heavier than a tennis ball.
As to anti-gravity, how do we invent such a thing when we don't really know even what gravity is? Perhaps once we develop a quantum theory of gravity, and/or reconcile the equations of general relativity and quantum mechanics involving it, we might be able to do something in that direction. But we're years, even decades, away from solving those problems, and until we do, we can't even think about inventing any kind of anti-gravity device.
And even if and when we do, it will still require enough energy to counteract that 0-100 kph in 2.8 s to float. Any kind of transportation capable of enabling a human being to soar through the air like a bird for hours while running off a mobile phone battery isn't going to happen, now or in the future.