The crew should have delivered their own payload first. Then, if it didn't work (which they would have known right away), they could return to Icarus I and retrieve that payload for a second chance. They kept talking about two chances, not doubling their chances, so they can't have meant to fire them both at the same time. These characters were chosen for this mission because they are the best and brightest in their fields available to Earth's space exploration program, and they all think long and hard about whether the benefit outweighs the risk before deciding to alter their trajectory to dock with Icarus I to get a second payload, so this cannot be considered a "character mistake." In this way they are not risking the mission at all. They may not have enough fuel to return home after all that backtracking, but that is admitted to be less important than successfully delivering the payload. Also, if they were able to stop and dock with Icarus I then continue on the way they were shown to, then they could just as easily dock with it having come from the other direction. Pinbacker could still cause problems, but they didn't know he'd be a threat when they were making plans. [Sorry, but this is an opinion, nothing more. If the Icarus was damaged during an unsuccessful initial attempt, then there would be no way to go back to get the second payload. If they want to guarantee the second chance, the best option is to pick it up on the way there, rather than getting there, trying it, failing, turning around, going back, getting the second payload, returning to the launch point, all of which involves potential danger. Unnecessarily complicated, when the far simpler solution is just to bring both payloads along and only have to make one approach to the launch point rather than potentially two.]

The crew was sent on a high-risk mission, not a suicide run: It is made very clear that no part of the Icarus II may be exposed to the sun without it being destroyed. What exactly was their plan for getting home after they detached the payload? They deliver the stellar bomb, the shield goes with it. True, they are all considered "expendable" in terms of saving humanity, but their original plan involved returning home. [The large shield we see for most of the film only needs to be that large to cover the payload area, which is by far the largest part of the whole ship. Once the payload area separates from the rest of the ship, you can see there is a much smaller shield (concave instead of convex) which is suitably sized to protect the comparatively much smaller ship. The reason the ship burns after separation is because nobody is piloting, so the ship turns sideways and is exposed to the sun.]

In order for a star to die, it must first go through a "Red Giant" stage, after which it would either become a dwarf star or implode, thereby creating a black hole. Nevertheless, Earth would be destroyed in the Red Giant stage because the stars growth would envelop the planet. [The trivia section of imdb.com says the sun is not dying "in the normal sense". It is a bit wordy: http://uk.imdb.com/title/tt0448134/trivia.]

When they have to travel through space from the Icarus I to the Icarus II, one of the men must remain to open the lock gate. Why don't they choose the man with the spacesuit (Capa) to open it? He could do it and after that, fly to the other spaceship. [Capa couldn't do it as they needed the decompression of the airlock to give them to momentum to fly across.]

There's something a bit unfortunate about the name "Icarus". Why would they give the spaceship a name of a Mythological character who died because he approached too close to the Sun? [By what stretch of the imagination is this a movie mistake? Just because you think something's "a bit unfortunate"? So the choice is slightly ironic - it's still entirely appropriate. The ship is going way too close to the sun for comfort, exactly as the mythological Icarus did.]