I second Ed Brayton's thoughts. I'm sure Moore's columns will provide much future entertainment and fodder for us.
Seriously though, I think, in this past post, I answered the basics of what Moore writes in his introductory column. I'll expand a little here.
First, Moore could argue that as a matter of constitutional technicality, he was in the right (although, the way our system works is that state courts must obey federal court commands, and if you think a lower federal court erred, you may appeal the case to higher federal courts, up to the Supreme Court of the United States, and make your case there). In fact, Moore does argue this:
As the former chief justice of the Supreme Court of Alabama, I lost my position because I chose to follow God and the United States Constitution, our rule of law, instead of a federal judge's unlawful order commanding me to remove a Ten Commandments monument from the rotunda of the Alabama state judicial building.
There are a couple doctrines which some serious constitutional scholars advance that suggest on originalist grounds, Moore's case didn't involve an Establishment Clause issue (and we'd have to get 5 Justice Thomases on the Supreme Court and wait for such a ruling to come down in order for Moore, as Chief Justice of a State Court, to get to lawfully keep his monument, though). For instance, the argument that the Establishment Clause is a federalism only provision. Or if anything is incorporated against the states, it is an individual right to be free from coercive establishments, things that actually "pick the pockets or break the legs," (a metaphorical phrase for real harm) of individuals. If a rock displayed on public grounds with a religious message doesn't actually harm you in any real sense, then no Establishment Clause issue is raised.
If that were the proper way to understand the Establishment Clause (as Justice Thomas argues), then not only would Moore be able to keep his rock, but...a Muslim Judge could erect a monument to Allah, a Hindu Judge to Shiva, a Pagan Judge to the Greek and Roman Gods of Justice, (all of them could argue that our rights come from such divine sources), or an atheist Judge could erect a monument which says "under no God" and no Establishment Clause issue likewise would be implicated.
But that's not what Moore was fighting over. Indeed, if Moore understood the issue in that respect, I don't think he would have bothered with a fight which ended up destroying his career. As he writes:
But my case was not about a monument and it was not about the Ten Commandments: It was about the acknowledgment of the Judeo-Christian God as the sovereign source of our law, liberty and government.
What Moore actually did was misunderstand and betray our Founding Fathers (Washington, Adams, Jefferson, Madison, Franklin, et al.) who never identified God in their public supplications as the God who revealed the Ten Commandments to Moses. They replaced the Biblical God with a generic "Nature's God," and the Ten Commandments, with the Ten Amendments of the Bill of Rights. If Moore had simply erected a multi-ton monument of the Declaration of Independence with its invocation of a generic God and Divine Providence and also featured the Ten Amendments of the Bill of Rights on the stone (and nothing more), I wouldn't have had a problem with that. And, if you want to challenge strict secularists who want no mention of the Divine in the public square, that would be a test case which correctly understands Founding history and political philosophy.
Also, there is no such thing as the "Judeo-Christian" God as Jews and Christians worship different gods. The Christian God is triune in nature, while the Jewish God is not. Moreover, the Founders didn't use the term "Judeo-Christian" and otherwise did not try to make any kind of coalition, or draw a lowest-common-denominator between Jews and Christians only. Back then, though the colonies varied in which particular religious sects received rights, the two strongest competing philosophies were that which held Protestant Christians only ought to receive the full rights of conscience and that which would grant rights universally to those with creeds no matter how unorthodox. Our key Founding Fathers fell into the latter. In other words, they would grant Jews full rights of conscience along with, in Jefferson's words, "the Gentile, the Christian and Mahometan, the Hindoo, and Infidel of every denomination."
To repeat, you will not find the key Framers -- Washington, Adams, Jefferson, Madison, Franklin -- identifying God exclusively as the God who revealed the Ten Commandments to Moses or the God of the Bible. Now, their generic monotheistic God could be, in the minds of private citizens, the God of the Bible, or some very unorthodox Providence. But He (or She or It) is not so specifically defined. Even when Washington addressed the Jews and noted the God whom they worshipped -- "Jehovah" -- was the same "Wonder Working Deity" in whom he believed, he said so as a religious universalist who customarily referred to God in specific terms used by those he addressed (Washington never used the word "Jehovah" when not speaking to Jews as far as I know). Indeed, when speaking to the Native Americans, Washington, Jefferson, and Madison (perhaps Adams, I haven't yet found his quotations as I have with the other three), referred to God as "The Great Spirit," just as the Indians did.
If you want to say that the Founders' "Nature's God" is the God in the Bible, the best you could argue is yes, He is with one serious caveat: He is the Biblical God except for everything written in the Bible about Him which didn't comport with their understanding of Man's Reason, like His irrational wrath and jealously. These Founders believed the Bible was errant; it contained in Adams's words "errors and amendments" (or in Jefferson's, its history was "defective and doubtful") and Man's Reason was the penultimate tool for determining which parts of the Bible were legitimately revealed by God (as Jefferson put it, Man's Reason could find the "Diamonds" of Truth among the "Dunghill" of error contained in the Bible) and which were not. Everything that didn't passed the "Reason" smell test was thus properly edited from the Bible. And doctrines like the Trinity and the Incarnation were the most unreasonable "corruptions" of Christianity which, as John Adams put it, "stupified" the minds of the Christian world. Adams went so far as to tell Jefferson that even if God Himself told him the Trinity were true, he wouldn't have believed the doctrine because 1 is not 3 and 3 is not 1, period. And both Jefferson and Adams explicitly doubted that the Ten Commandments were in fact revealed by God.
Somehow, I don't think the likes Roy Moore think such a God deserves worship or public acknowledgement. But Jefferson and Adams (along with the similarly heterodox Ben Franklin, and two other lesser well knowns) were the men who actually wrote the Declaration of Independence.
It's a pity Moore doesn't properly understand the Founding. If he did, he might still have a job.