When Data informs the Captain of a similar event having taken place on Captain Kirk's Enterprise the computer graphic shows a model of the refit-version of a Constitution class Starship. But Kirk had to deal with the Psi-2000 virus on his first five year mission (Star Trek: The Naked Time), way before the refit of the Enterprise, which did not occur until Star Trek: The Motion Picture. This has since been corrected in the 2012 remastered edition, with the correct graphic of the TOS-series Enterprise graphic featured.
When Picard and Crusher are talking in his ready room the camera zooms into their faces very close. They are standing just a few inches apart and Picard can be heard giggling. Not only is giggling inappropriate (Picard has not been infected) but his lips seem to move as if he were saying something.
Correcting Commander Riker's wording, Data mentions the correct term for what happened to the science ships's bridge crew from "sucked" (Riker's term) to "blown". Actually, the term "suck" is defined as a fluid or mass traveling from a high pressure region to one of low pressure so Riker's statement about them having been sucked out was factually correct.
Dr. Crusher is upset and worried when Riker touches her, after he got infected himself previously. Yet whenever treating La Forge, the first person to be infected, at no time does she wear gloves or any other type of protection for herself, which a good doctor in the given situation would normally always do.
Data is affected by the virus, and notes that his android physiology and mechanisms leave him susceptible to such illness. In future episodes, notably Angel One, Data is seen as being immune to plagues and viruses affecting human crew members.
At the moment Tasha Yar infects Deanna Troi by holding her hand, the scene shows 2 camera angles (1 from over each characters shoulder). From Tasha's perspective, we see the blue garment she was inspecting last is held between both characters right hands, but from Troi's perspective, the garment is clearly shown being held only by Tasha in her left hand.
Yar uses the phrase, "Ship's stores will have it." With replicator technology there would be no need for storage. Any item needed could be replicated, from food to clothing to spare parts. No need to store clothing. You'd place dirty clothing in the replicator and turn it into new clothes. Recycling on the atomic level. However, it should be pointed out that replicators, like shuttlecraft when "The Enemy Within" was produced, had not yet been introduced in the series; they would not make their first appearance until "Conspiracy", towards the end of the first season.
After the Chief Engineer McDougall is called to the bridge the assistant Engineer Shimoda is then called to medical. Both calls false of course as Wesley issued both to get control of Engineering. I find it hard to believe an Engineer or even an assistant Engineer would leave a child in charge of Engineering.