The Leonov crew's triangular mission patches show both the Soviet and U.S. flags, but the U.S. flag is upside-down: the stripes are on top and the stars are on the bottom. Flying a flag upside-down is only supposed to be used to signal a dire emergency... but the reason there are Americans on this mission is precisely because needing to rescue Discovery before it crashes into Io is a dire emergency.
There's also a bit of a poke at the nature of the mission in that patch: Effectively, "This is a Soviet mission and don't you Yanks forget it."
Moiseivich: A Russian craft, flown by Russians, carrying a few poor Americans, who need our help. That also would look good on the front page of Pravda.
When David says "something wonderful" is going to happen - he means it literally: something full of wonder.
In 2001, Dr. Heywood Floyd seems to be a "company man" - he even tells the Moonbase staff that "formal security oaths" will be required to keep their mouths shut about the Monolith. The 2010 Floyd is a cowboy. Being blamed for the failure of the Discovery mission, the loss of the crew, and still not knowing what happened burned him out. So he won't take crap from anyone. It would explain why he was so eager to defy Milson's order not to work with the Soviet crew.
The significant changes of the EVA suits from their very close-conforming shapes in 2001 may be just more than the changing styles of sci-fi set and prop design. After Frank's murder in the first film, aerospace designers all over the world would recognize the folly of having an astronaut's/cosmonaut's sole oxygen supply fed by a single external hose to their helmet without backup, and remind them of the serious risk of micrometeroid collisions (or EVA pod collisions!), which would lead to bulkier suit designs more in-line with IRL designs.
