The real HMS Archer is not an attack submarine; it is a patrol boat.
When the Coxswain is having the decontamination shower you get a quick glimpse he is wearing underwear and not naked which he should be in a real decontamination situation.
All the Royal Navy personnel on HMS Vigil are wearing radiation monitors yet Amy Silva is not issued one while moving around near the reactor.
When Amy is writing the note for her daughter, the audio indicates that she makes just a few strokes with the pen. Yet when the paper is shown, she's drawn a picture of a bird comprised of far more lines.
Surgeon Lieutenant Docherty treats the injured coxswain alone. Royal Navy ballistic missile submarines have at least a Medical Assistant on board.
It is highly irregular for all submarines communications to be disabled especially SSBNs. They carry back up communications systems or reached by Extremely Low Frequency radio.
The submarine's doctor suggests to the coxswain that, in the event of poisoning by a nerve agent, the antidote might include atropine. However, she pronounces it "AE-tro-peen" instead of "AT-ro-peen", which is an error inappropriate for the character's knowledge base.