The Cigarette Smoking Man has a tracheostomy. He should not be able to speak unless a special device were attached to the tracheostomy (not apparent in this episode). Generally, a tracheostomy has to be covered to allow someone to speak. Please note that the word "tracheostomy" refers to the placement of a tube in the trachea while "tracheotomy" is just the act of cutting into the trachea. "Tracheostomy" is the correct term in this use.
The anthrax vaccine is a cell-free filtrate of the B. anthracis bacterium, meaning it does not even contain whole bacterial cells. It is utterly impossible for administration to result in disease.
At 5mins 5sec, Scully is at Mulder's desk whilst he is away. She turns on his laptop by just pressing a key. In an organization like the FBI, computers would have timeouts that lock the machine after say 30secs of inactivity.
At 16mins 14s Agent Einstein gets out her smartphone and immediately starts scrolling without having unlocked it. There is no sign of her entering a code, or even passing a fingerprint scan to unlock it.
At 16m 41s almost everyone appears to have the same make, if not same make and color, of umbrella.
At 13m 29s the road sign indicates Mulder is entering South Carolina from the northeast (first Spartanburg, then Greenville 33 miles later.) The sign indicates there are 88 miles to Spartanburg, when in reality Spartanburg is about half that distance from the border with North Carolina.
Scully refutes Tad O'Malley's claim about everyone having alien DNA and she turns out to be right, but in the Season 6 premiere The Beginning (1998), she states that everyone has a genetic remnant or junk DNA that matches the DNA of the alien claw and the alien virus.