Problem 1 (minor): God lied, which makes it okay for us to lie if we are adhering to the qualities of God which are by definition Good.
According to the tradition, God did not lie (and this seems a reasonable interpretation): They died both spiritually and instigated the process of decay/mortality entering the world, which leads eventually to physical death.
Another minor problem is that God tries to prevent Adam and Eve from obtaining knowledge whilst Satan encourages them to attain it, showing that knowledge is an evil thing that should be avoided.
That's only a minor problem... because it's based on your assumption that Satan was morally right and God was not.
Look at it this way: If you already have the truth, then more knowledge is not needed, and in fact knowledge can only tempt you, confuse you, and lead you AWAY from the 100% spiritual peak you've already attained.
For INTPs and others who automatically start with knowledge (rather than authority) as a basis for moral decision making, this seems wrong.
Problem 2 (major): Original sin had not been committed by Adam and Eve because they did not have the knowledge of good and evil in the first place. If knowledge of good and evil (which derives from the tree of knowledge) is what provides one with the concept of morality, and morality is strictly adhering to the 'good' side, while sin is indulging into the 'bad' side, what fault had they committed by eating from the tree which they knew not was a 'bad' thing (only after eating from the tree would they know that the action was a sin, they had no knowledge of it beforehand)? This is a big problem, because it implies that God created humans with sin in the first place, they did not bring it upon themselves through free will (ignoring the fact that the omnipotent God would have already known that Eve would eat from the tree).
I haven't read the other responses yet, due to time constraints; but this has always been a flaw to me as well and why I see the story as allegorical, as a way to "explain" the bad choices of humanity, rather than something literal. (Mythical stories always have "flaws" like this if you try to analyze them in the wrong way and not just focus on what need they were serving in the community.) The cause/effect process here in the story is circular and "chicken/egg" like, not linear; it doesn't follow; they already had the capacity to sin.
But I suppose it would be approached like this in the theology: Adam and Eve had at the ability to sin inherently but hadn't yet sinned and thus were still pure; ability to sin is not the same as actually sinning; once they chose to sin, then they were no longer pure and sin entered the world.
Another approach is to say that, while they had the ability to rebel (and did), they did not have knowledge of sin in the sense of a moral external checklist, it was much more intrinsic and organic than that. Once the Tree incident happened, morality became codified and thus detached from living in the moment. People could rebel against the moral statute, rather than it being this attraction/repulsion directly to God.
To put it another way, if you ran across a notorious rapist, you would probably feel some sense of repulsion... because you'd see his actions as evil. This response is intrinsic, not calculated; you don't think, usually, "This man is a rapist; rape is wrong; therefore I must despise him." You instead feel repulsed first, then figure out why later.
However, the Fall allowed people to codify morality so now it COULD become less of a repulsion of the rapist and now more an accessing of the rule list -- "Rape is wrong; therefore I must despise rape." There is a detachment from the internal response. People are separated from their own internal moral core. Their relationship with God is now also legislated, not internalized.
That is another way to look at it.
