The Gemini launch was actually pretty accurate. That squeal noise heard just as it begins to launch is a result of the engine's starter cartridge firing up:
I don't know if it'd be that loud in the spacecraft, but that's what it sounded like.
I saw it on Friday and thought it was very very well done. I agree that Neil was made to seem very blah and unemotional, which, with what we know about him, is not entirely accurate, but it was still very good.
The cinematography was beautiful (though a bit shaky). The launch and landing sequence were phenomenal, some of the best I've ever seen in any film, and when they showed the iconic skirt separation in the launch, my mind exploded. They really nailed down those details.
The soundtrack, IMO, was perfect. It really set the tone of triumph, hope, and aspiration, but also made you experience the same dread and hurt that the movie itself portrayed.
Overall, for a nonfiction film, Apollo 13 and this one are tied for me. For nonfiction, interstellar and 2001 still beat this one, but that's because there's more leeway in the story of course.