I liked Avatar, but to me the obvious science fail was the telepathic connection between the Na'vi and the animals. Evolution doesn't work like that! Rattlesnakes do not grow rattles for your benefit! I'm afraid that yon astrophysicist knows rather a bit more about physics than about evolutionary biology if the inter-species universal complex adaptations didn't jump out at him.
As for the planetary tree-mind being able to read out human brain networks using its own standardized equipment, who are they kidding?
Yes, the whole plot would have worked without it! The central tree could have been providing a vital nutrient without which the local ecosystem would fail, or something that their women needed to reproduce. There's no reason you need telepathy to ride a horse. The final stampede could have been started by one or more heroes, rather than being magic. And the final body-swap wasn't really necessary (just keep using the old equipment), but it could have been an effect of running the interface for a sufficiently long time (the alien brain gets reprogrammed).
And then it would have been hard science fiction, which would have made a visually-awesome, okay-plot movie into one of the greatest SF movies of all time.
Also, I will accept pretty alien ladies for the sake of plot, but having them cry tears is going too far, and it's not necessary. That really jumped out at me.
Avatar was good, but it could have been so much more if they'd spent five minutes thinking about how to get the plot effect they wanted via science instead of magic.