Stupidity: This highly prepared organisation knows Dracula is coming, but comes armed with guns they're not prepared to use, and allow him to grab a weapon and shoot one of them. Then they give him a tablet but assign the most basic of passwords to the Wi-Fi, rather than disabling it entirely, or even just giving him a Kindle, given the only point of it was access to books. Plot-serving idiocy.
Other mistake: At the end, when the reflection of burned Lucy still shows her beautiful, Dracula's reflection shows him as he is seen; not old and ugly as in his usual mirror reflections.
The Rules of the Beast - S1-E1
Dracula: I'm undead, I'm not unreasonable.
Blood Vessel - S1-E2
Trivia: The secretive room on the ship with a dark secret is cabin no. 9. Mark Gatiss, co-writer of this series, also co-wrote another creepy BBC series called "Inside No. 9"