Aragorn in Moria?

[Kuruharan]

As far as I recall, there are only two entrances/exits into Moria (not counting the Endless Stair). Am I off on that? The West Gate and the East Gate.

I would phrase it that "we know of two entrances." If I remember correctly, Gandalf said "a door" when referring to the West Gate not "the door" which implies there were more gates on that side of the mountains.

However, if these were the two most known entrances, it is probable that Aragorn would have used one of them...and since Aragorn clearly didn't know how to enter from the west, he must have entered from the east.

I actually like how the movie presents Gandalf as advising against the entry into Moria. I don't understand how Aragorn would know not to enter, while Gandalf was unsuspecting to the danger that was within. Perhaps Gandalf knew he was supposed to fall there. I don't know. But from a logical standpoint, it makes more sense to me that Gandalf knew the evils of Moria in the film, rather than in the book where he seemed clueless.

I disagree with this. I think Gandalf knew something of the dangers (remember that, in spite of what the movie said, nobody knew what Durin's Bane was) but he thought that it was a risk worth taking. Also remember that when the Wargs attacked, everybody suddenly agreed with him, including Aragorn.