The Engineering Officers should hold the rank of Lieutenant Commander not Lieutenant, unless he is Deputy Engineering Officer.
After surfacing the Captain sees a 'stealth' tanker bearing down on the sub. (it must have been a stealth ship or they would have heard it on the sonar, no excuses). He orders the boat to dive narrowly missing a collision. Had he ordered a dive turning to port or starboard the issue would have been resolved with much less tension.
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.
In the first scene where Kirsten is being stopped from leaving the base, the reflection of the cameraman is clearly visible in the rear window of her car - one of the disadvantages of using a vehicle with tinted windows.
As the Surgeon Lieutenant treats the sailor caught in the nitrogen burst, she does it alone. Royal Navy ballistic missile submarines have at least a medical assistant.