2001 A Space Odysessy and my take on the failure of the HAL 9000

So if you have never read the novel or seen the movie 2001 A Space Odyssey, this post will not make a lot of sense or have much meaning.  Recently for some reason I have been really trying to answer a question about this movie, and that question is does the HAL 9000 purposely lie about his move during the chess match with Frank Poole or does he really make an error?  For this argument I want to only focus on the movie version and not the novel because I think the novel gives too much to make a conclusion about the question and the real question is why does Stanley Kubrick leave things so vague. 
Let me give a little background into the mystery of the question.  HAL, the computer, is supposed to be fool proof and incapable of making errors.  HAL is on board a space ship with 5 human crew members, 3 are in a cryogenic state and 2 are awake and managing the ship, though HAL is really doing all the hard work and the two crew members are just going through the motions.
The reason for this trip is known by HAL and the 3 crew members in cryogenic sleep but not the two awake crew members.  They are going to the Planet Jupiter to make contact with an alien life form of some kind.
During the trip HAL plays a game of chess with Frank Poole, one of the astronauts.  During a chess match between the HAL 9000 computer and Frank Pool,  HAL tells Frank that Frank has make a bad move which would allow HAL to win the match.  But the moves that HAL recites to show his win is all but certain is actually wrong according to fact that Kubrick seems to have used the tournament game between A. Roesch and W. Schlage, Hamburg in 1910 as the game that we see HAL and Poole play.  Many people have stated that Kubrick was a very good chess player himself and so he would not have written the chess move that HAL makes incorrectly.  But one question I keep asking myself is does HAL make this move on purpose to test Frank Poole or does HAL make the move accidentally because he is starting to have issues due to his programming?  The issue is this- if HAL makes the statement on purpose, he is lying to Frank and therefore he has made an error.  If he make the statement incorrectly he is faulty and therefore still making an error. One reason people think that HAL makes this mistake is because he has conflicting orders and he does not know how to process this.  He is built to not distort information from the crew but by not telling the 2 astronauts what the true mission is all about, he is distorting information.  Now granted, the crew never asks HAL directly, "what is our true mission" because they may think the true mission is to get the 3 sleeping astronauts to Jupiter and that they are hibernating to save on resources like oxygen and food.
I have been reading a lot of people's opinions online and it does seem that people have researched the hell out of this topic.  The consensus seems to be that HAL is testing Frank and later Dave Bowman to see if they are really know the true meaning of their mission or maybe if they are capable of handling the mission at all.   But lets say that HAL said the chess moves in error and Frank says "Hey HAL, that is wrong, you made a mistake."  HAL, a computer who is incapable of making mistakes, would now be suspect by the awake crew members that the computer could be failing and placing them in some danger because HAL controls all the life support for all the crew. They would probably want to disconnect HAL from running the ship.
My personal feeling is that HAL would not be testing the crew to see if they know the true meaning of the mission because HAL was already told that the awake crew doesn't know the true mission.  The same holds true when HAL is asking Dave Bowman a lot of questions about the secrecy of the mission.  Dave Bowman does not give any indication that he is aware of the missions true nature so why does HAL figure he needs to kill off these two guys? If HAL didn't do anything, they would reach Jupiter, the 3 crew members that are asleep would be wakened by HAL and then they would all do the mission.
There is some other things in regards to the crew and HAL that I thought was very strange in the movie.  HAL reports that the AE-35 unit which controls the antenna that points it toward Earth is going to fail and recommends that they replace it with a spare unit.  Dave Bowman takes a shuttle pod and goes outside of the ship to retrieve the failing unit and replaces it with the spare.  This unit is then tested and it is determined that the unit is not going to fail.  HAL recommends that the first unit be placed back into service and then they can wait for it to fail (HAL tells them he knows it is going to fail in 72 hours) and this time Frank goes out in the space pod to do this. During this trip, HAL kills Frank while he is outside of the pod by cutting his oxygen tube.  Why didn't he kill Dave bowman while he was on his trip outside of the space pod first.  Also prior to Frank being killed, Frank and Dave go into a pod to talk about what is happening with HAL without having HAL listening in.  They enter a pod, HAL is asked to rotate the pod to the non-launch position, Frank and Dave turn off the audio channels to make sue HAL cant hear them, and then talk about HAL's failings.  HAL is able to see them talking about deactivating him through the pod's window, but this would not have happened if Frank and Dave never rotated to pod around so HAL could see them.  I cant seem to think of any reason why Stanley Kubrick thought the POD they entered through a hatch that was facing HAL had to be rotated 180 degrees  so now HAL could see them talking.
Another thought is that after Dave Bowman realizes that Frank Poole has died out in space he tried to retreive the body by using another pod to get to Frank, but HAL will not let the pod back into the ship in one of movie's most famous lines "I'm sorry Dave, I'm afraid I can't do that."  Hal knows at this time that the 2 astronauts are going to deactivate him because he made the error and they are concerned, and he probably thinks that Dave will go after Frank, thereby leaving the ship and he can now run the mission, but then I am still not sure why he kills off the 3 astronauts in the cryogenic sleep.  HAL could have woken them up and said that the other 2 died trying to fix the antenna and that's all.  Or HAL could have turned the Antenna away from earth so no contact could be make between the ship and earth until HAL could put all his plans together.
So what is my conclusion on all the questions I have?
I believe that HAL made an error in the chess match, and was probably happy that Frank didn't catch it. I think that HAL now knows he made a mistake and has to kill the crew to cover up the mistake because he knows the mission and he cant tell the crew that but he also knows he alone can complete the mission.  I think Dave and Frank made a huge mistake when they ask HAL to rotate the pod to face him, had they not don't that, HAL would not have known the plan to deactivate him and the crew would probably all have survived and fulfilled the mission.  I do wonder though if HAL had thoughts about being th eone to touch the monolith and evolving like everyone else that did so be fore him.