In this movie, Heywood Floyd has a much more down-to-earth and blue-collar personality than his officious, patrician portrayal in 2001. Although this could easily be explained by his fall from grace due to the events of the first film.
We also don't really know if Heywood was telling the truth when he claimed he didn't know about HAL's secondary instructions.
2010 gives us the explanation in the novel as to why Hal went crazy.
Hilarious in Hindsight: Dave Bowman's widow is seen wearing an off-the-shoulder Flashdance-style T-shirt. These actually came back into fashion in the real 2010.
Dr. Floyd's son has a poster of the Olympics in his bedroom reading "Beijing '08" at the bottom. For added flavor, keep in mind that this film was made in 1984, and that the IOC wouldn't declare Beijing host of the 2008 games until... 2001.
Memetic Mutation: ALL THESE WORLDS ARE YOURS EXCEPT EUROPA. ATTEMPT NO LANDINGS THERE. USE THEM TOGETHER, USE THEM IN PEACE.
"You see, something's going to happen." "What?" "Something WONDERFUL."
Humorous variations on the title of the film were used quite a lot as newspaper headlines in the year of 2010.
Nightmare Fuel: When Heywood tells HAL that he can't do something drastic without knowing who's sending the message, HAL replies, "He says, I understand. It is important that you believe me. Look Behind You." The orchestral warning and the Oh Crap! look on Heywood's face makes for a seriously spooky moment. And then, all the stuff that follows...
The creepily distorted version of Bowman's "My god, it's full of stars!" that plays right before the recap.
Surprisingly Improved Sequel: Some feel 2001 was a great artistic achievement, but even some of its fans admit that it can be ponderously-paced at times with wooden characters and a lot of Scenery Porn. 2010 was a better movie for the masses (and some scifi fans) in that it was much less artistic and more accessible.
Vindicated by History: Time has freed the baggage of the film as a sequel to Kubrick's work, and it's much more appreciated now, especially with the separate questions it raises about human nature and life.