Factual error: Alicia realizes that the asteroid is actually a comet by its tail. However, earlier in the episode we are told we are far from any star (so no point in opening the solar sails). The thing is, comets only develop a tail when they are near a star, which blows gases off the comet with the solar wind (the same wind that could operate solar sails). So in reality, there would be no tail to this comet.
Factual error: When asked how the shuttle will move the large space ship, Alicia says, "We're in space. There's no gravity, resistance, or friction. Size doesn't matter, just force." However, Newton's second law still applies in space. F=m×a, or a=F/m. The acceleration is in direct ratio to the force and opposite ratio with the mass. In other words, given the force the shuttle's engines can apply, and the very large mass of the space ship, the acceleration the shuttle can produce is relatively small. (00:25:56)