When Bowman fades from wife's TV they an ad for travel to Sri Lanka is on. That is the chosen home of Arthur C. Clarke.

Dr. Floyd is talking to Victor Milson on a bench in front of the White House. Near the end of their conversation, the camera is positioned so you can see an older man sitting on the bench next to them. . . which is Arthur C. Clarke himself. Also, the voice of SAL is Candice Bergen. The voice of HAL is Douglas Rain who was HAL's original voice in 2001:A Space Odyssey.

In the nursing home scene, the nurse at the desk is reading Time magazine. The cover concerns the US/Soviet conflict integral to the plot. If you look closely, the US President's picture is a colored drawing of Arthur C. Clarke and the Soviet Premier's picture is a colored drawing of the director of 2001, Stanley Kubrick.

An interesting scene to watch is when Heywood Floyd is talking to his associate on the bench in front of the White House, there is a long shot when you can see a person feeding pigeons. It is none other than Arthur C. Clarke in a cameo appearance.

In the scene where they are Airbraking , they are hauling super fast around the planet , but you can see stuff dripping from the fireball straight down.

The conflict on earth is between the U.S. and the "Soviet Union". The film takes place in 2010 but the Soviet Union dissolved in 1991. Since the film was made in 1984 the writers wouldn't know this.