It is stated that Mrs. Royce's car was tracked via EZ-Pass, leaving Staten Island going into Manhattan, through Brooklyn via the Verrazzano-Narrows Bridge. In reality, there is a one-way toll on the Verrazzano-Narrows, leading into Staten Island, not leaving it. Therefore, it would be impossible to track a car leaving Staten Island that way, as a car can't be tracked by EZ-Pass going from Staten Island to Brooklyn.
Cordite is a type of smokeless propellant developed in England in 1889 as a cleaner burning more efficient alternative to black-powder (gunpowder), it was mostly used by the British, Canadian and Australian military through World War II. After that due to shortages of materials needed to manufacture Cordite, and the Olin Corporation in the United States developing smokeless gunpowder it fell out of use completely by the late 20th century. Since Cordite was never used in the United States and had been all but replaced with smokeless gunpowder by the 1960's it seems unlikely that a suburban civilian would have a gun chambered in a British cartridge and highly unlikely that he would have access to ammunition loaded with Cordite. Also it's stated that the gun he has is .44 caliber and we saw that it's a revolver meaning it has to be a .44 Magnum since he stated that he bought the gun recently, there are no other .44 caliber revolvers in production currently, and it makes no sense for him to have ammunition loaded with Cordite since the .44 Magnum was developed by a U.S. company after the development of smokeless gunpowder, meaning there was never any production .44 Magnum ammunition loaded with Cordite. Also doesn't make sense that Olivia and Elliot would know what it smells like considering they weren't even born yet when Cordite was still widely used in munitions and only then in the U.K. and Canada.
Law enforcement agencies cannot access the Armed Forces DNA registry without first getting a court order from a Federal or military judge, and in order to get a court order law enforcement needs at least some evidence showing that the suspect is a member of the Armed Forces. So it is partly incorrect when Olivia says that they can simply run the DNA from the rape victim against the Armed Forces database to identify a suspect, they would need evidence that their suspect is a member of the military. More evidence than the victim being killed by having her neck broken using the subluxation technique as this evidence is weak and circumstantial because this technique is used by many different country's armed forces and is also used by certain martial arts forms.