I realise these may have been addressed earlier in the thread, but I wanted to make a clean break.
Burden of proof arguments
Actually, you're misinterpreting the way that the burden of proof is actually used in a logical sense - that is, the burden is on the person making an affirmative statement. It's not semantics, it's actually an important logical principle. Hence, Russell's Teapot (which, as I'll explain later, you haven't actually refuted).
If a theist wishes to propose the existence of his god, then they are making an affirmative statement. Atheism in its weak form is actually just a passive position that makes no assertions. In fact, strong atheism actually makes very little logical sense because it is logically impossible to prove that something does not exist. Therefore, since the theist must make an affirmative statement about the existence of their god, the atheist simply needs to reject their proposed proof in order to demonstrate that the theist's claims are untrue.
Further, the existence of God is often (in my experience, always) presented as an unfalsifiable and untestable position. The "god of the gaps" has no actual meaning when you are continually reducing the gaps and yet finding nothing. If you cannot test for something it makes no sense to talk about it as a statement that relates to actuality, let alone the practices of organised religion.
Furthermore, if you will not reject the notion of god based on the lack of proof, then you must also accept the existence of other things with similar amounts of "proof", such as the existence of ghosts, the soul, the Greek Pantheon, muses, angels, spirit auras, Allah, Thor, Odin, the invisible pink unicorn and so on. This quickly demonstrates how flawed this position is.
It sounds ridiculous
You would be right that to reject an idea purely on the grounds that it is "ridiculous" is not sound. However, an important principle in rational skepticism is that the more outlandish or ridiculous the claim, the more evidence you are going to need to support it. For example, if I tell you that I am typing at my laptop in my girlfriend's kitchen to write this post, you probably don't need to bother gathering a lot of evidence to support that claim. However, if I tell you that I am in fact typing this post by patching through the British Telecom system from a spaceship orbiting a little-known moon of Sesefras Magna*, it might take more proof to convince you.
Carl Sagan's quote, "Extraordinary claims require extraordinary evidence", which paraphrases Hume's Maxim ("No testimony is sufficient to establish a miracle, unless the testimony be of such a kind that its falsehood would be more miraculous than the fact which it endeavors to establish"), is an important tool to consider when looking at the world. Check out this link (
http://skeptico.blogs.com/skeptico/2008/01/extraordinary-c.html) for a more in-depth discussion of this idea.
*Kudos to anyone who gets this reference.
Historical contradictions
If there is a direct contradiction between two events (for example, the Genesis account(s) and what science has established about the history of the world), then one account or the other is incorrect. Perhaps not entirely incorrect (as, you mention, with courtroom testimony), but on the details one must be correct and the other incorrect. You cannot have two mutually incompatible accounts that are both entirely accurate. If you want to modify the literalism of the biblical accounts, then you're guilty of special pleading.
The Invisible Pink Unicorn
As I've already pointed out in the other thread, this is argumentum ad populum and hence a logical fallacy. Russell's Teapot stands.