Theoretically, it is not really that hard to imagine something that would disprove those. The big bang can easily be disproved by demonstrating that the universe is not expanding. This would however be almost impossible to show in reality, but only because you would also have to show that the enormous amount of evidence which shows the exact opposite is wrong, not because big bang is somehow inherently unfalsifiable.

No, lying witnesses don't give you information.

One of the fundamental principles of relativity is the fact the speed is relative, which makes it meaningless to speak of something have a speed without also saying what that speed is relative to. The only thing that matters here is our speed relative to Betelgeuse.

As a rule of thumb, relativistic effects (time dilation, etc.) can pretty safely be ignored at less than 10% of the speed of light. Here's a graph illustrating how time dilation increases with speed, if you're interested: http://www.thebigview.com/spacetime/tdgraphformula.gif

The gravitational forces within a galaxy are more than strong enough to counteract the effects of the expansion of the universe, so the distance between Earth and Betelgeuse is completely unaffected by it.

Long answer: Dark matter wasn't invented just because someone saw some anomalous behavior that didn't agree with theory, and said to themselves: "Oh, there has to be something mysterious at work here, we'll call it dark matter.". There are several reasons for believing in dark matter, for example that when measuring gravity we notice gravity coming from directions where we can't see any matter. However, the source of this gravity behaves a lot like matter would. For example we can observe these "invisible gravity sources" being thrown around when two galaxies collide. Because these "invisible gravity sources" acts a lot like matter, except for the fact that we can't see it, it's called dark matter.

If you're not yet convinced, take a look at this recent blogpost by a professional astrophysicist: http://scienceblogs.com/startswithabang/2010/11/the_simplest_argument_for_dark.php In this post, he basically explains how we can derive the existence of dark matter from: A) Assuming that the theory of general relativity is valid, B) assuming that the big bang theory is valid, and C) our observations of the cosmic microwave background.

So a few asteroid impacts every billion years or so? There are probably many other things that are more dangerous than that.

If you had read the article you would know that they did precisely that.

After a quick search on the internet I found plenty of counter-examples to that claim. One example: "For God commanded, saying, Honour thy father and mother: and, He that curseth father or mother, let him die the death." (Matthew 15:4). How is telling people to kill disobedient children not condoning violence? Perhaps you should try listening to you own advice: