Episode #1.1 - S1-E1
Continuity mistake: When David meets the Home Secretary for the first time outside her car, he is wearing a grey shirt. In the next scene (in the lobby) his shirt is white, before turning grey again later.
Character mistake: When the bodyguards enter elevators, they always enter last; they should be entering first to ensure it is secure. This is particularly visible in the hotel where the elevator can stop on any floor and Special Protection Branch does not have complete control of it as an express.
Episode #1.6 - S1-E6
Trivia: In the park where PS Budd is surrounded by armed tactical response officers, a careful observer would notice that the brand of ear protection devices the officers are wearing are Z-TAC, an airsoft brand.