When Carol gets in the Jaguar, we see the tachometer red-line before we see her first step on the accelerator. When you first switch on any car with modern computerized (as opposed to merely electronic) instrumentation, during its self-check the gages all swing full-scale and back to zero before beginning to register.
When Dr. Bennell, a psychiatrist (who of course are also physicians), is rifling through the pharmacy looking for drugs that will prevent sleep, she never even thinks about Provigil, the standard anti-narcolepsy drug also used by the US Air Force to allow pilots to stay awake and alert for extreme periods of time. This medication almost certainly would have been any doctor's first choice.
When Carol receives a call in Ben's Jaguar after escaping the pharmacy, we see the cellphone in the foot well; it's Carol's Nokia 'candy bar' shaped phone. However, she says "that's Ben's phone". Next, we see her talking into Ben's flip phone. For the rest of the scene, she's using her own Nokia phone.
In the background where Oliver and his friends encounter an agitated dog and the the owner who is apologizing for the dog's odd behavior, a boy dressed in a Superman costume, a girl dressed as Dorothy from The Wizard of Oz, and an adult dressed as a clown, can be seen already in the process of crossing the street and passing off screen to the right. As Oliver and his friends were leaving the house, the same people in the background are shown further back than before and just beginning to cross the street.
When Carol arrives at the office in the morning, she sits down by her computer to do some research on the virus. Her secretary comes in and offers her a cup of tea, but as Carol picks it up to take a sip, the cup has changed into a mug.
During the Subway scene the exterior is initially shown to be the DC Metro. As soon as she's on board the subway, she's in the interior of the Baltimore Metro. When the brakes are applied, a quick exterior shot shows an Amtrak Acela train (which she rides later in the movie) coming to a stop in a tunnel, before finally reverting to the exterior of the Baltimore Metro when she escapes through the cab door.
When Carol is in the pharmacy and finally falls asleep, she drops the large bottle of soda she's holding, which spills all over the floor next to her. When her son finds her and injects her with the epinephrine, and they stand up together, the spilled soda and the bottle are no longer present.
When Carol gets on the Amtrak train in DC to go to Baltimore, as she gets onto the train, behind her is a sign that says "This station: South Station/Next station: Back Bay/Destination: Washington, DC."
The Amtrak Acela Express goes from Boston to DC (via Back Bay).
When Carol is in her office and is discovering that certain diseases make people immune to the virus, she states that the white matter in the brain being changed is what provides immunity. When she phones the Biologist and tells him her theory, he agrees with it. However, when repeating her idea back to her, he says that changes in neurons are what provides immunity. White matter is not composed of neurons, however, and these words are not synonymous.
During any news coverage, they show the correct MSNBC logo and on screen (with MSNBC being a full horizontal shaped logo). However, when reporters are seen at the end of the movie, "one year later," they have a microphone flagged with the "L" shaped MSNBC logo, (MSN stacked vertically, NBC horizontally) - which hasn't been used since 2005.
When the space shuttle Patriot is making its fatal plunge into the atmosphere, the three main engines are ignited. These are fueled by the large External Tank during liftoff, and are inoperative once the ET drops away 9 minutes after launch.
When Carol is in the pharmacy, she easily grabs a gun from an infected policeman's service holster. However US policemen carry guns in locking holsters that prevent removal unless done in a very specific way. Her first attempt to grab the gun would have been unsuccessful.
When Carol is reviewing Wendy Lenk's medications, she incorrectly pronounces clonazepam (clo-naz'-uh-pam) as "clozepan" (clohz'-uh-pan). Any psychiatrist (or medical student) would know how to properly pronounce this commonly used drug's name.
After Carol and Oliver enter the pharmacy, Carol lifts Oliver onto the counter and he barely slips through a gap in the security gate. Carol is then shown attempting to do the same. The movie then cuts to behind the counter and she jumps down. Although it appears that she would not fit (and hence this being regarded as a goof), actually the security roll is deformable. This is clearly visible when she pulls on it to get up on the counter (particularly on her left hand side) revealing that a gap through which she can easily fit can be created.
In the introduction, when Carol is rifling pharmacy shelves looking for medicines to keep her awake, she says "Clonazepam, good." Clonazepam (better known in the US by its trade name, Klonopin) is an anti-anxiety drug with a sedative effect, not a drug one would take to stay awake. However, her child was also on anti-anxiety drugs, and there was a 50/50 chance that it would render her immune.
When Tucker and his group of friends chase Carol and Oliver down the alley, they clearly show frustration (a form of anger, which is an emotion) once they cannot find the two. Yet, Tucker and his friends have already been infected with the alien virus, to show no emotion.
When Carol and Oliver enter the elevator, she hits the button for the 29th floor. This causes the button 29 to light up. Yet a wide shot of the elevator interior a few seconds later reveals that neither 29 nor any other floor buttons are lit.