(at around 50 mins) Searle's statement about 80% of dust being human skin is a commonly held, but false, urban myth. Common household dust on Earth is composed of many different things, and none of them individually account for anything close to 80% of it. Given the situation, it's entirely possible that the dust he's looking at is mostly human skin, but this is not true for dust in general.
(at around 29 mins) Cassie turns the Icarus II to 'generate shadow' for the repair to take place, but the computer animation on the screen indicates the intended maneuver won't take any part of the shield out of sunlight.
Critical damage is caused to Icarus II by sunlight reflecting off a communications tower onto the structure. Yet, when Icarus II approaches Icarus I - much closer to the sun - its shield reflects sunlight onto the rear of Icarus I with no ill-effects to that ship at all.
(at around 14 mins) Near the beginning of the film the ship is said to be 36 million miles from the Sun. The large images of the Sun that the crew see are therefore obviously greatly magnified, as at that distance the Sun wouldn't appear that massive to the eye. However that distance is closer to the Sun than Mercury's average distance, so the planet should appear much larger than it is shown. However Mercury has quite an elliptical orbit, and it's possible that at the time, Mercury may have been near its closest point to the Sun, which is 28.5 million miles (7.5 million miles from the ship). Even so it would still appear much larger relative to the Sun than it is shown when it passes in front of the Sun's disk.
(at around 7 mins) As pointed out by one of the characters, the ship enters the "blackout" area around the sun (and loses contact with Earth) anomalously early, before Mercury's orbit in fact. Communications from this close to the sun are not a problem in reality (and were possible with 1970s technology), but the writer and director took deliberate creative license to improve the tension.
(at around 32 mins) When the end of the rotating com tower gets fried by sunlight, it leaves a trail of burning debris behind it (opposite its direction of motion). This would happen only in a planetary atmosphere; in the vacuum of space, the debris would appear to drift straight away from the end of the tower in the direction it is pointing.
(at around 2 mins) At the beginning of the movie the ship is 36 million miles from the Sun, and thus the Sun would appear about (93/36)^2 = 6.7 times brighter than it would on Earth. But the computer says that at 4% transmission through the screen, the Sun would cause eye damage - despite being four times fainter than it would appear on Earth (and we know that in the story the Sun at Earth is fainter than we observe it today). Still, at 36 million miles, the Sun would only be about 1.3 degrees in angular size - much smaller than one's fist at arm's length.
In his DVD commentary, director Danny Boyle says the original idea for Icarus I was to "be on its side, like the Zeebrugge". In fact, he is referring to the "Herald of Free Enterprise", the British ferry that capsized on 6 March 1987 while leaving the Belgian port of Zeebrugge. 193 passengers and crew were killed.
(at around 29 mins) As the crew attempts to rotate the shield to repair it, there is an argument that they would lose com towers 3 and 4, which they say would need on the way home. However, many shots including the simulation of payload delivery reveal that the Icarus' small shield which is supposed to protect Icarus after the payload is detached, just isn't wide enough to protect those towers at all, so they would've lost them anyway. It is even questionable, whether this shield would be capable of protecting the Icarus itself after detaching the payload with the large shield and at that close distance from the sun.
The goof items below may give away important plot points.
Errors in geography
(at around 1h 40 mins) In the final scene, the western side of the Sydney Opera House is seen in the background, viewed from a parkland. There is no parkland west of the Opera House. That area is the old suburb of Sydney called The Rocks. While set 50 years in the future, The Rocks would not be converted to parkland as it is full of national heritage buildings. The scene was filmed in Stockholm, Sweden, and the Opera House was added later.
(at around 1h 2 mins) During the "space jump", one of the crew members freezes solid in a couple of minutes. Space is very cold, but objects in a vacuum cool down extremely slowly. The heat in the object has to go somewhere. On Earth, the heat would be transferred to the cold surroundings, such as the air, by contact. In a vacuum, there is nothing to transfer the heat to, so objects that are warm stay warm for a long time. This is the principle behind vacuum flasks. The only way an object in a perfect vacuum can cool down is by electromagnetic black-body radiation. A person would radiate about 1000 Watts (57 BTUs per minute) in this situation, which is only about 7 times more than they would radiate in a 68° F (20C) room.
(at around 1h 3 mins) During the spacewalk scene where Capa, Mace and Harvey are trying to get back aboard the Icarus II from Icarus I, they float across into the airlock. The shot cuts to the airlock control panel, which indicates "Equalise", whereupon Capa and Mace immediately crash to the floor of the airlock as it's re-pressurized. This wouldn't happen; gravity operates whether there's an atmosphere or a vacuum, and once they were inside the gravitational field of Icarus II (however it works), they'd have literally "fallen" to the floor immediately.
(at around 1h 2 mins) Two of the crew members jump from the Icarus I to the Icarus II without space suits. Contrary to expectations created by B-movie science fiction, this is entirely possible. The human body simply does not have enough internal pressure to explode in vacuum. Air in the lungs is expelled almost instantaneously, provided that the subject doesn't attempt try to hold his/her breath. Blood is contained and held under pressure by tension from the walls of the circulatory system, so it has has no way to boil. A prepared individual can remain conscious for more than ten seconds, and stay alive for for several minutes, in a complete total vacuum. One NASA engineer involved in a vacuum chamber mishap has discussed the sensation of standing exposed in vacuum until he lost consciousness, from which he recovered completely.
Towards the end of the movie, the critical issue was that there wasn't going to be enough oxygen to reach their objective, let alone get back to Earth. However, the payload area was also pressurised and contained a huge volume of air. The amount of oxygen contained within that area would have sustained the surviving crew for more than long enough to complete their mission.
(at around 1h 12 mins) As Capa asks the computer about the crews vital signs she informs him that he and the entire crew are dying. Within sixteen hours the crew of five would be dead due to asphyxiation. She also informs Capa that they are nineteen hours away from the sun. As Capa learns about Pinbacker being aboard the ship, he runs into the observation room and fights with Pinbacker. He is stabbed and locked in the air lock and Pinbacker messes with the mainframe. He then contacts Mace and the events precede linearly from there, with no obvious long skips in time. This would mean the fight with Pinbacker lasted nineteen hours until they reach their destination in the sun, which is clearly not the case leaving a seeming 14-17 hour gap in the storyline. In short, what happened to the predicted nineteen hour trip?