Why didn't HAL just cut off the oxygen in the entire ship and kill everybody on board, instead of the overly-contrived mechanics of lying about a malfunctioning piece of equipment and sending someone out on a spacewalk so he could do it physically and singly (and with no plan as-of-yet for the other remaining member); I can understand him not having any movable "weapons" to do it with inside the ship (hence why he'd require them to be outside)... but he shouldn't need to bother with *ANY* of that if the oxygen supply control is under his command(which it almost definitely certainly is)?
This actually happens in the original novel. After HAL kills Frank, Dave tries to revive the three crewmembers in hibernation at which point HAL opens all the doors on the ship to create a depressurization with the intent of killing everyone. While he does kill the three hibernating crewmembers Dave is able to survive and subsequently deactivate HAL. Also the malfunctioning antenna is explained away in the novel as part of HAL's neurosis, not only needing to cut himself off from Earth in order to resolve the conflict of interest introduced by conflicting orders, but also to keep the crew from telling them what was happening. The depressurization probably wasn't included in the film version because of production values (although an early draft of the script did include it) and also we would never have gotten the iconic "Open the pod bay doors" scene.
An early draft of the script actually had the depressurization scene from the novel. As the troper above said it was most likely scrapped due to technical and/or budgetary reasons.
How did the humans know that the radio signal transmitted by the Monolith on the Moon was directed at Jupiter? If it was a narrow-beam transmission, and it took the humans by surprise, they shouldn't have been able to detect it at all unless there happened to be an antenna between the Monolith and Jupiter. If the Monolith was broadcasting the signal, it wouldn't have been aimed anywhere in particular. And what would the Monolith have done if it had been dug up during a time when Jupiter wasn't visible in the sky?
Who's to say there wasn't? There could have been any number of satellites orbiting the Moon, Jupiter, or both at the time. And why do you believe that the signal "wouldn't have been aimed anywhere in particular"? What would be the point in sending a signal off in a random direction into deep space? Finally, presumably the monolith would have just waited until Jupiter rose to transmit its signal; keep in mind that the monolith had already been unearthed for some time by the time Floyd et al. got to it.
I meant that the Moon Monolith could have broadcast the signal omni-directionally, and the Jupiter Monolith could still have picked it up, but the humans would have no way of knowing that it was aimed at Jupiter. Since night on the Moon is 14 days long, the Monolith in Tycho had been unearthed for several days, but it wasn't until Floyd arrived that it first became exposed to sunlight, which was its trigger to send the radio signal.
The beam had 2 purposes. 1) alert TMA-2 that an intelligent species had evolved and developed technology to a level needed to find and unearth TMA-1 2) Force said species to figure out where TMA-2 was by tracking the beam. An omnidirectional beam doesn't fulfill the second objective. Possibly the Monolith would rebroadcast the signal every few years if the species wasn't able to figure out where TMA-2 was due to not having satellites in the right position to track the signal or rebury itself if it had been unearthed by something like an asteroid impact.
In the novel, the signal is intercepted by four satellites - two orbiting Mars, one in the asteroid belt, and a deep space probe heading for beyond Pluto. It's not a narrow-beam radio signal, but "an immaterial pattern of energy, throwing off a spray of radiation like the wake of a racing speedboat".
Furthermore, the monolith was being researched with the highest priority by the present scientists. It's very probable they had a whole range of probes surrounding the thing, trying to gather as much information as possible (including its electromagnetic spectrum).
How Communist were the Soviet Union cosmonauts, and did they have to pay for their phone calls to earth? If they didn't, wouldn't the Americans sneak in and use their phones?
They probably had it as a job perk, and the Americans weren't allowed to use it unless they, presumably, got trade credit (or whatever Soviet communists euphemistically call it) and got permission from the people who were authorized to give them permission (assuming the Soviet phones were even compatible with Pac. Bell's systems). If the cosmonauts felt like letting the Americans make calls from their line, but weren't authorized to do so, they still couldn't let them because call information from the space station would have been monitored. About the "Wouldn't the Americans sneak in" part, you clearly have a low opinion of Americans in The Future (if not in general).
These are Dirty Communists, and the KGB is probably monitoring every call. That's why the Americans wouldn't want to use the Soviet phone system.
Although the first movie is rightly seen as one of the hardest science fiction movies ever made, there are still a few things that don't make sense. For one thing, it's all very impressive that Kubrick figured out how to get a stewardess to walk on the ceiling, but what fool would really design a ship like that? There's a reason why modern spacecraft and space stations are designed with very clearly defined walls, floors, and so forth; having to perform a maneuver like that on a regular basis would be needlessly disorienting, to say nothing of what they expect to happen when the ship enters the moon's gravity well and the pilots are suddenly strapped upside down to the ceiling. (I can let the first issue slide for obvious reasons, but the second one can't really take that much of a logical leap, can it?) For another, the movie can't seem to settle on whether artificial gravity exists or not; yes, both the space station and the Discovery use centripetal force to simulate gravity, but you'll notice that when Dave and Frank are on Discovery's bridge, they walk around normally even though there's no possible way it can be spinning. I'd buy that their boots may use the same technology as the stewardesses' "grip shoes," except that their feet clearly aren't sticking to the floor and they aren't using the bizarre "one foot at a time" gait that the stewardesses use.
Although they simply could have had magnetic floors and boots, like in Tintin, you may also have noticed that the interior of that sphere doesn't fit inside it (due to the size of spherical EVA vehicles). What could have Kubrick mean by this is unclear, however.
It doesn't quite match up correctly in execution, but the stewardess has to do her little walk upside-down because the bridge of the lunar ship is facing forward, allowing the pilot to look out the front, while the passenger section is oriented so that when the ship lands they are upright. The pilots aren't "strapped to the ceiling" - they are, in affect, strapped to the floor when the ship lands on the moon, facing upward out the windows.
And there is no artificial gravity - there would be no need for the centrifuge (the big wheel set) in Discovery if they had artificial gravity. Dave and Frank never actually walk around on the bridge. They do move around a little too freely in the pod bay, which should be in zero-G, but the idea is that they are sticking to the floor with grip-shoes (there are velcro strips carpeting the set for that very reason). Maybe they're just better at using their grippy shoes than the stewardess earlier in the film was.
The real puzzle is why everyone in Clavius base on the Moon is walking around in what is obviously Earth-normal gravity.
The apparent Earth-level gravity on Clavius is a production oversight, similar to how Dave leans on HAL's console in the pod bay which is a zero-g environment. As for the quicker movement with the grip shoes by Dave and Frank, a possible in universe explanation is that in the time between the "Blue Danube" sequence and the flight of Discovery the technology had been improved to allow for more freeform movement (remember the Monolith was found on the Moon in 1999, and Discovery is sent off to Jupiter 18 months later in 2001). Also if you look at the bridge for Discovery, the two cockpit seats are actually angled downward due to it being a zero-g environment.
The cockpit seats are set so that while the Discovery is firing her engines they will be pushed down into their seats instead of in some other direction.