Other mistake: Taylor believes he is on a planet 300 light-years from earth for most of the movie. However, after spending months there, he would have seen the moon at night a number of times, letting him know where he really was before seeing the Statue of Liberty.
Suggested correction: Not necessarily; any astronaut knows that many, many planets have moons, so Taylor could have easily thought that it was simply an odd coincidence that the "other" planet's moon closely resembled Earth's moon.
Character mistake: A space traveler would not be "going to Orion." The major stars in Orion vary in distance from the earth from 243 to 1,360 light years. Orion is only a constellation as visible from Earth; once you get away that far, the stars would not be in the same alignment as they are from Earth. They would have been going to a specific star, probably Bellatrix at 243 light years, as Taylor mentions being at 320 light years.
Suggested correction: I'm not sure what scene you're referring to, but I never heard anyone say they went to Orion. Taylor says they're on a "planet in orbit around a star in the constellation of Orion. That could be Bellatrix." To Taylor, who is from Earth, the star is still in the constellation of Orion.
I agree with your take, but I still think it could be interpreted as Orion's stars all being in close proximity. And I would hope they would know about the 320 - 243 light year issue.
