In The Martian, Mark makes water using a couple of things. I'm not sure if I saw it correctly, but it seemed to me that he took the rover and drove to the rocket to get fuel from it. However, isn't that the rocket the other crew members used to fly to the bigger space station? In other words, did the writers screw up and let Mark use fuel from a rocket that had previously left Mars?
He didn't. He used the hydrazine tanks from the MDV (Mars Descent Vehicle) - emphasizing that the descent vehicle is completely separate from the MAV (Mars Ascent Vehicle), which is what the crew used to leave at the beginning of the film. Like the MAV IV (which Watney used to leave Mars), the MAV III had been sent in advance of the mission to create fuel, so they didn't depart in the same ship they arrived in.
From the book, "Log Entry Sol 30":
The MDV has 292 liters of juice [hydrazine] left in the tanks. Enough to make almost 600 liters of water!
Yes, this is from the book but the same was done in the film.