To answer your questions, we need to look at how D&D 4th edition is defining alignment. It is defined as the moral stance of the character. I believe it is fair use to quote this short excerpt.
Good: Freedom and kindness.
Lawful Good: Civilization and order.
Evil: Tyranny and hatred.
Chaotic Evil: Entropy and destruction.
Unaligned: Having no alignment; not taking a stand.
Each of these has a detailed explanation in the 4th edition Players Handbook.
In addition the players handbook goes on to explain the distinction between alignments and a character's personality.
Reading about Lawful Good we see that the Players Handbox has two parts to the alignment, one that authority is good because it effectively prevents harm to life and promotes the quality of life.
Absence one of those two ideals then the character has another alignment. If he believes in authority but not in the sanctity of life then he would be considered evil. He may not be a tyrannical control freak, that is a personality trait. By 4e's definition he is evil because the character is willing defend authority regardless of the consequences on individual lives. The degree in which he does so is dependent on the individual characters personality. If he doing things out of consideration for his own benefit then he is unaligned.
It seems to me that in 4e, Lawful Good, and Chaotic Evil are extreme moral positions. That Good, Unaligned, and Evil are the categories most people fell into.
Personified forces of nature (chaotic neutral), aka Greek mythology,
which, while dangerous, are not necessarily evil?
Unaligned, while they are not operating like a character they are doing things for their own benefit in accordance to their nature.
The honorable lawful evil villains, who offer their opponent a fair
chance in a duel?
In 4e such a character would be evil.
Moral dilemmas where there is no obvious good and evil choice?
This has nothing to do with alignment as alignments are description of an aspect of a character.
Possibilities for intrigue and conflict when a lawful neutral
inquisitor-type character has to cooperate with a chaotic good one, to
defeat a great evil.
A inquisitor type committed to his moral code without regard to the sanctity of life would be considered evil under 4e definitions. There is nothing that would really prevent him from working with a good alignment character if their goals align. But there would be potential conflicts.