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.
The crew wraps itself in insulation foil, as a protection from the cold of space. Later a body freezes stiff within minutes after being exposed to space. Someone got a freeze burn within minutes. This is quite nonsense, because the heat of the body is actual thermal energy, that needs to be transferred, in order for the body to cool down and freeze. Since there is allmost no matter in the vacuum of space, there is nothing to transfer the heat energy to. The thermal energy would just radiate away, which would take many hours to freeze. Also for this short time space exposure they could as well have been naked, without any issues.
(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 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 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.
Early in the movie the crew sees Mercury transit the Sun. (Transit means it passes between the Sun and the observer). Mercury is seen crossing the entire orbit of the sun from the observer's point of view. Mercury rotates the Sun every 88 Earth days. It was moving extremely fast compared to its orbit around the Sun.
(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 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.
At the beginning of the film, Icaruss II tells Searle (Cliff Curtis) that viewing the sun at 4.0% its actual brightness would do irrevocable damage to his eyes. However, when Pinbacker (Mark Strong) is revealed to have survived on Icarus I and is attempting to sabotage Icarus II, his skin is severely burnt from viewing the sun at a higher intensity, which would mean that he would be blind, though this is not the case.
When they go to investigate Icarus 1, there is complete darkness on the ship. After Pinbacker stops the coolant to the main computer, and AI shuts down, there is complete darkness on Icarus 2. When they were going to the Sun which is the ultimate fail safe source of the light, they should have made some arrangement to use sunlight itself to provide light to both the ships, using some transparent window or some optical device that picks sunlight from the surface of the ship and transmits to every area inside the ship, to give all or some of the lighting.
In the interaction with Capa, Icarus AI that is monitoring and controlling the ship reveals that it was aware of the presence of a fifth unknown person on the ship, consuming scarce resources. Why didn't the ship manufacturer hard code the names and identifications of all authorized crew members to Icarus AI, and program her to report to these crew members if any other "unknown" person is location on the ship?
(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. Moreover, the crew of the Icarus I apparently committed mass suicide early in their mission (when they reached Mercury), and dead people do not produce new skin cells. And even then, Searle should be able to deduce that the inch-thick dust over everything could never have accumulated from the skin cells of such a small crew - dead or alive.
(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.