I had a professor who was into kite photography, which I’d imagine would have some of the same issues. There’s a bit in the wiki about stabilization - basically, you use a gravity-based stabilizer - and some links to other sites. The Goodyear site says they fly around 1000-1500 feet for visibility, with a max of about 5000 ft. That’s really not high enough that you’d be getting major air turbulence - it’s less than a lot of mountains, for instance. You would have issues with cloud cover, but other than that, I’d say it’d be about the same as any long-distance photography.
Actually, a significant number of shots in movies are taken from helicopters. I’m not sure how high they fly, though. And I’m not sure how close they zoom in on something on the ground.
There’s no real difference between looking down from 1500 feet, and looking horizontally from 1500 feet = roughly 1/4 mile.
When a camera at one edge of the stadium zooms in on somebody clear across the stadium, that’s about 600 ft at most. And you don’t see many shots like that because the zoom isn’t quite good enough to make people large enough to be a compelling picture.
We’ve all seen closeup shots of the moon taken from a stadium during a game. They can zoom that to fill the screen. And the picture is steady and very clear despite going through the entire height of the atmosphere, not just 1500 feet of it. But consider sitting at one end of the stadium as the moon rises over the other. How much larger is the moon than some guy’s face behind the opposite goal post? Answer: a LOT.