Visual effects during airflights and space flights
This being one of my all-time favorite movies, I've literally watched it at least a dozen times, if not more.
I saw it as a kid and I was amazed by it. Almost 30 years later, it still stands up 100%.
One of the subtle things I took for granted when I first saw this as a kid that I don't necessarily do now are the repeating theme of visual distortions that you see from the eyes of the pilots and astronauts. It looks very psychedelic, with blurry moving lines and swirls.
You see it Yeager's first flight when he breaks the sound barrier. Then in his second X1-A flight when he's going after Crossfield's record and he blacks out for a second, you see it manifested like a black hole vortex. Then after Shepard reaches space, you briefly see it, and again during Glenn's orbit. And finally it shows up again during Yeager's F-104 flight.
Back when I was 9 or so and I first saw it, I somehow thought that's how things actually looked when you broke the sound barrier or flew into outer space. Looking back on it now, I think it was more of a heavy stylistic choice, but a really cool looking one.