As T'Pol is reprimanding Trip, in a close-up you can clearly see that half of her eyebrow is brown paint rather than hair. Also the color doesn't quite match.
This is the first contact with a new species, that the Vulcans don't even know about, so the universal translator wouldn't have their language in the database. Yet somehow, both species are able to speak the same language.
The Vissian chief engineer tells Commander Tucker that a polymer used on their ship is made of more than 200 naturally occurring elements. Tucker is shocked because the Earth database show only 92 naturally occurring elements. What's wrong here is that at the time of filming there were already 94 naturally occurring elements discovered and not 92 (as of 2017 94 plus 24 synthetics elements for a total of 118 ).
The game of Go played by Tucker and the Cogenitor doesn't make much sense. The "winning move" shows the Cogenitor actually losing a point by playing inside its own territory.
Archer tells Drennik that William Shakespeare only wrote 36 plays. Actually, the number usually given is 37 or 38. There is some dispute about this, as it is not always agreed whether The Two Noble Kinsmen, of which Shakespeare only wrote part (and just how big a part is unclear), should be included. In addition, there are believed to be 2 or 3 additional plays that Shakespeare wrote but were never printed and have thus been lost to us.