The dance in Singin' in the Rain with Kelly is unbelievable. They were both incredible. You don't have to be a dance fan per se to watch and be amazed and appreciate the tallent there.
I heard Charisse interviewed once and they talked at length about that very dance. She and Kelly practiced some bits and pieces of it a few times, but decided to roll film on the first take (a potentially-expensive decision in those days). They nailed it. What you see in the film is the first and only take.
In movies today, very often, when you see a dance sequence, there's a lot of camera cuts and very little pan and zoom. This is the modern directing style, sure. It's enabled by the fact that cameras are smaller and cheaper today and film costs a lot less. You can afford to have a few dozen cameras filming from every angle. BUT, there's another reason they make all these cuts: you can splice together the best bits from as many takes as is required to get at least one good pass on every step. And with digital editting, you can even fix minor errors. So, a typical dance scene in a movie today is a splice and dice from dozens of takes aided by digital editting and special effects.
Not this one with Charisse and Kelly. They only had two cameras, but the cameras follow the action, panning and zooming. Edits are very few because they were done by hand with razorblades and tape and each could take a half-hour to get perfect. So, it's just them, Charisse and Kelly, and they danced the dance from first step to last perfectly on the one and only take, no digital editting, no computer-generated effects.
Charisse also said in the interview, that that was the first and only cigarette she smoked in her life. And notice how she handles it, with grace and drama. The cigarette, the glasses, the hat, even her dress are as much a part of the dance as Charisse and Kelly. She also noted that being lifted by Kelly felt like "nothing, like just floating up, effortlessly."
What you're seeing here is what there is very little of in Hollywood today; what you're seeing here is REAL talent.
They just don't do it like that anymore. It's a lost era. And now we've lost the queen of that era. How sad.