When Wikus is taken into hospital for the first time and sees his hand turning into a "prawn's arm", he freaks out and the doctor puts a mask over his mouth and nose to administer some oxygen and holds it with his hand. When the shot changes there is a rubber band holding the mask to his head, but there is no way that the doctor could have managed to put it that way.
In the scene where the MNU workers first walk up to Christopher Johnson's shack in order to evict him, the radio operator identifies the shack as "Yankee Foxtrot Five Three Zero," or YF530. However the number on the shack itself is FY530.
When the officers and Wikus' family and friends were talking, their titles and names were placed on the screen. When one of the MNU officers were talking, they misspelled LIAISONS, spelling it LIASONS.
When Wikus is in the sub-level MNU HQ firing range, and when they are fitting his HUMAN (right) hand to the AMR-B21 directed energy weapon, the thumb and index fingers have intact thumb and finger nails. In the office space after returning from field operatioms, Wikus picks at his right hand index finger and the nail falls off. He then visits the restroom where his thumbnail is pulled free when he tugs on [it] with his teeth. Both expose a red "quick". Then as mentioned above, the nails are perfectly manicured in the MNU HQ basement firing range.
When Wikus looks at his chest, he observes the black boils which were forming. However, in a later scene, when he is caught temporarily by the soldiers, he has a clean chest (except for the blood from other bodies on him)
After Wikus is ejected from the badly damaged mecha suit, he lands on a flat dirt area with litter all around him and starts to crawl slowly. When the camera comes back to him, he's crawling through dried up brush and there is a fire near him. When the screen reads "74 hours after exposure," he is again crawling on a dirt path with no vegetation or fire around him.
In the scenes following the escape from the MNU facility, the team hunting Wikkus is shown is from an AgustaWestland Merlin helicopter. In the next scenes the helicopter is an Aerospatiale Gazelle (the cabin shots are clearly from a Gazelle judging from the size of the interior).
After Wikus escapes from the bio lab, he is seen removing his clothing including what appear to be a pair of espadrilles. After stealing replacement clothing, his new footwear are exactly the same as those he wore during the eviction scenes.
In the scene where Wikus first meets Christopher and attempts to get his signature on the Eviction Notice, the pen on Wikus' clipboard is attached with Velcro and can be seen switching from parallel to angled and back again several times between shots.
When Wikus is first admitted to hospital and is having his arm checked, it is quite clear that he has a hairy chest under his vest. Afterwards, he is seen with his shirt off and is hairless. Because the surgeons are planning on opening his chest to remove his heart, it is likely that his chest was shaved in preparation for the procedure. Another reason may be, due to the changes his body is undertaking (fingernails falling off, etc.), his hair may have fallen out.
Everyone has modern mobile phones. However, the movie is not actually set in the 1980s. This is the date of the aliens' arrival. The events of the film are approximately 20+ years later, and on-screen date stamps put the movie explicitly in the year 2010.
When the mothership activates, the Mecha suit performs an automatic defense program to protect Wikas who is now shown as a "Prawn". However, when Christopher is also under attack just a few moments later the suit does nothing.
The goof items below may give away important plot points.
Incorrectly regarded as goofs
Early in the film, we are told that people cut a hole to force their way into the spaceship. (The spaceship is thought to therefore no longer be space-worthy for Christopher's voyage at the end of the film.) However, the full mechanization of the space craft is unknown, and the affected area could be sealed off from the rest of the ship.
Christopher Johnson has collected the alien fluid for 20 years and is shown to distill the final drop - making him ready to use the spaceship. However Wikus Van De Merwe accidentally sprays himself in the face with some of the fluid, making the canister not full again. Still Wikus and Christopher can fly the spaceship without distilling more fluid. This may not be an issue however as originally Christopher was not going to leave Earth right away and he wasn't going to leave alone, he may well have been collecting a greater amount of fluid in order to carry a significantly heavier load, namely the entire Earth based Prawn population, he also may have planned other mother-ship activities before he left meaning, when his plans changed he may well still have had enough fluid left to fly the ship home.