As mentioned in Character Errors, despite being told by Malcolm to turn the insert clockwise Jonathon begins turning it counter-clockwise, then in a subsequent shot he is turning the insert clockwise as instructed.
Lieutenant Reed reports that mine is magnetically attached to the hull of Enterprise. If a spaceship were to be constructed of metal, it would most likely be a lightweight, yet strong metal, such as titanium. Titanium, and other lightweight metals, have almost no magnetic properties, the mine certainly wouldn't have stuck to the hull of the ship if were made of such a metal.
When the two Romulan ships come to tell the Enterprise to detach the deck plating and leave the system immediately, the Romulan states that they know there is one crewman trapped on the outer hull and eighty-two others aboard. However, Archer is outside with the trapped Reed at the time the Romulan makes this statement.
At breakfast, Archer and Malcolm briefly discuss the soccer/football World Cup. The World Cup takes place every four years and this episode takes place in 2152. There wouldn't be a World Cup tournament that year. However, being set 150 years into the future allows plenty of time for there to be a change in the current schedule - especially since WWIII was fought in the 2050s in the Star Trek universe. In real life, the 2020 World Cup was postponed until 2021 due to the COVID pandemic.
An occasional bug can be seen flying by when Reed and Archer are working to defuse the mine. There would be no bugs flying around where there is no atmosphere.
In Balance of Terror (1966), set in 2266, the Federation did not know that the Romulans have a device to "cloak" their ships and weapons. If the NX-01 reported it in 2152, the NCC-1701 would have been expecting it.
It's quite conspicuous that nobody thought to use the transporter throughout the episode. It could have been used to retrieve Reed, even while he was pinned to the ship's hull. It especially would have been useful to retrieve Archer and Reed instead of them enduring the preposterously dangerous manoeuvre of using shuttlepod plating to protect themselves from the blast (which should have killed them both instantly considering the power the first mine did to the ship).
The explosion at the end would most likely have killed Archer and Reed instantly considering the power of the first mine earlier on. Even if that wasn't the case, both men would have been flung so far in different directions in the vacuum of space that Enterprise could not have retrieved them so quickly afterwards.
English people usually say anti clockwise rather than counter clockwise although things can change by the 22nd century.
There is no reason why the crew couldn't have just beamed Malcolm back into the ship, even despite the mine sticking into his leg. Of course, that would have made the story a lot shorter.
Malcolm tells Captain Archer to turn the wheel on final protrusion of the mine clockwise, but when we see Archer turning it, his hands clearly move counter-clockwise.
Hoshi listens to a recording and repeats the term Romulan but noticeably mispronounces it prompting T'pol to correct her. Being a prodigy with languages, it is unlikely that Hoshi would grossly mispronounce a word she had just heard.