Other mistake: This comes up in other sci-fi scenarios too - the shuttle is heading down to the planet's surface through heavy cloud cover/disturbances. Everyone acknowledges it'll be a bumpy ride, and the flight down is very fast and tense, trying to keep track of escorts, etc. But there's no need for it to be a fast entry. Their ships aren't aeroplanes which have a minimum speed and have to keep moving forwards. They could just hover and lower slowly through the clouds at a safe speed.
Other mistake: The hypodermic needle is in 3 different positions without being touched. One point it is angled, one is right next to papers and straight, and another it is below the papers. (00:36:50)