When Alan Krumwiede is explaining what an R0 of 2 means on television, he claims that the number of cases daily will progress 2, 4, 16, 256, 65536 and so on. This is incorrect - this is the quadratic series, and would mean that by the fourth day each person is infecting 256 others, and by the sixth day 4,294,967,296 would have fallen ill. The correct progression would be the geometric; i.e. 2, 4, 8, 16, 32... He later claims that it would take a month for a billion people to fall ill - this number is clearly based on the geometric number series, not the quadratic.
When Dr. Cheever leaves Roger's house after vaccinating Roger's son, the first shot shows his car parked on the wrong side of the street, with a huge pile of trash only 3 feet in front of the car. In the next shot from Cheever's point of view, the pile of trash is on the other side of the street, across the street from his car, instead of in front of it.
During the preliminary press conference at the CDC, Boston is listed as one of the first infected cities. Later on, a map is shown of infected regions around the world. It indicates that the only regions of Massachusetts infected are those regions west of the Connecticut River. Boston is approximately 100 miles east of the Connecticut River.
Durban, South Africa, is listed as one of the first infected cities. Later on, a map is shown of infected regions around the world, it shows South Africa's west coast as entirely affected, but leaves out the east coast - where Durban is.
The disease in the film is highly lethal, affects a very large number of people and has a short incubation period. In reality an infectious disease must have a long incubation period and less lethality than in the film to facilitate a sustained transmission. The real case makes tracking much more difficult, which is a central part of the film, therefore the filmmakers had to bend the facts a bit.
When the 'virus structure' is explained by Dr. Cheever, just a protein structure is shown. What is termed as a receptor in green is just a phenylalanine (amino acid), only a small unit of a protein. Viruses have several proteins and proteins are built of amino acids, so what is shown can't be a virus at all.
When Dr. Erin Mears is in Minneapolis racing to isolate the infected IMM executive from the bus, she can be seen wearing an N95 mask with an exhaust vent, about to put a similar one on the victim to limit his infectiousness to others. Vented N95 masks have a one-way valve that lets exhaled breath bypass the filtering for easier exhalation. She should be using a non-vented N95 mask on the infected patient.
When Li Fai, the Hong Kong patient, exits the elevator on his way home, the two red Chinese characters on the wall means "the 10th floor", while the display of the elevator says it's the 9th. However, this is likely not a goof. Floor numbering has become quite confused in Hong Kong due to a combination of British numbering (ground floor -> 1st -> 2nd -> 3rd) and the Chinese system which counts the ground floor as the 1st. Also, due to other traditions in regard to the number 4, that number may be skipped when numbering the floors.
Right after Dr. Ellis Cheever announces that approximately 1 in 12 people will contract the disease, we see a montage of abandoned places from around the world. One of locations is a deserted office in what we would assume to be a deserted city. Unfortunately, several cars can be seen driving through the window on the right side of the office, depicting what one would see in a typical, bustling city.
The goof item below may give away important plot points.
When Dr Leonora Orantes discovers the identity of Patient Zero and her liaison Sun Feng stands by, Feng's polo shirt starts the scene inside-out. As the two start for the car, his shirt is worn appropriately. Then in the van it is inside-out again and then correct, repeating throughout that sequence of events.