Episode #1.6 - S1-E6
Factual error: When Commander Anne Sampson appears in her body armour she wears the rank insignia only worn by the Commissioner (a crown over a pip over crossed tipstaves in a wreath) instead of that worn by her own rank of Commander (crossed tipstaves in a wreath). She has apparently been promoted four ranks.
Episode #1.3 - S1-E3
Audio problem: When Julia Montague and her bodyguard David enter the elevator to go down, the pre-recorded elevator message says "going up." Subtitles show "going down." (00:22:15)
Episode #1.4 - S1-E4
Factual error: Budd survives shooting himself in the temple with a blank cartridge, essentially an impossibility.
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.