Contrary to what many think (and even Terri herself thought in the scene), even if the tether was long enough to reach Woody, she still had barely enough fuel to get back to REMO herself, not to mention that if he caught the tether, much of his inertia would've been transferred to her (he's heavier), meaning that she would've needed enough fuel to brake their combined mass and then accelerate it back in the other direction. Odds on, they both would've done a cannonball onto Mars.
Potentially doubles as Lethally Stupid from the Martians, who are questionably "benevolent" precursors that have built a security system that brutally kills you with a sentient-looking sand tornado if you send the wrong answer (and it even attacks you by ASSUMING you're trying to enter, like the radar signal Luke's team sent to scan the mountain). Could you imagine if another highly advanced alien race, say, General Zod's kryptonian scouts from Man of Steel came along, got attacked by the tornado, and then Zod got mad and decided to retaliate by using the World Engine to obliterate the whole structure?
The ending frames it as something beautiful, but think about it: it's been millions of years. Is there even a culture left at the place this spaceship is taking Jim to?
People have griped that Mars Recovery had inadequate shielding on its vital components, and that, if a micrometeor shower really had struck the vessel, there should have been multiple layers of protection and redundancy to prevent the explosion that occurred. However, it is pointed out in the movie that Mars Recovery is launching early in a roll of the dice attempt to rescue the survivors of Mars One, if any. One could reason that the vessel was still in its final stages of fitting and testing before setting out, and they figured what they had outfitted the craft so far would hopefully suffice. This also helps explain the other flaws, such as the computer needing oxygen to work. In other words, this very scenario of departing with a hastily-prepared ship is what NASA in The Martian was trying to AVOID.
