For a bomb that had been in a vault since the 40's there was absolutely no dust accumulated on it.
When Hassan and Bothroyd are driving to meet Sarah, engine noises can be heard, gear changes etc.., but they are in an electric car.
The zip ties round Hasan's wrists are clearly very loose and she could have escaped from them with little difficulty.
The bomb that DS Hasan reveals in a vault was, by implication, undisturbed in the vault since at least 1941. In which case, who installed the push button phone on the wall? It's a modern design and not a 1940s vintage.
However, given that this series is about time travel, getting a modern phone into an old vault is not the most far-fetched aspect of the plot. The bank employees merely believed what they were told, i.e., that the vault had been undisturbed since 1941. Those behind the plot owned the bank and had provided the key. They could easily have had access (with a duplicate key) and installed the phone.
You can clearly see the eyes of the father that died blink. Can't believe no one added this yet..