Bunny-Ears Lawyer: Sobriety and a conventionally professional attitude aren't his strong points. Fortunately, forensic science is.
The Coroner: Jackson's official role, although he has also been seen gathering information and kicking ass.
The Gunslinger: One of the few characters who even carries a gun (with good reason), and indeed he is marked as American more than once by it.
I Have Many Names: He's changed his name and skipped town when things got too hot at least once; it's implied that this is something of a habit for him. Though Matthew Judge does appear to be his original name, as his brother has the same surname.
Jerkass: He goes out of his way to sleep with Rose after learning that Drake was sweet on her. Did we mention the madam of the house is his wife?
Behind the Mask: It's not totally incongruous with his other appearances, simply something that never comes up in his antagonistic interactions with the H Division team, but his private tenderness and concern for his boyfriend in Threads Of Silk And Gold is quite sweet, as well as shedding some light on his earlier position on moral hypocrisy.
In the first episode, he gets into a physical scuffle with Reid and counters Reid's own attempts to shake him down by suggesting he knows more than he lets on about the man's Dark and Troubled Past and wouldn't be afraid to tell the wrong kind of people. Shady, manipulative smartass not afraid to employ underhanded methods when under pressure or just for kicks? Sounds like Best.
For the second season: Best adjusting his prosthetic in the mirror, saying wryly to himself "Who's to say you are not beautiful?".
A young Irish constable who transfers to H-Division from Bloomsbury.
Dark and Troubled Past: He was "A little Paddy wretch, destined for jail or an early grave" before he joined the police.
Driven to Villainy: He has to do Shine's bidding, because Shine's in possession of Flight's damning criminal record. Though for the most part, Shine's kept him in the dark about how he uses the information Flight supplies him with.
My God, What Have I Done?: Twice. First when he realises that Shine must have killed Joseph Merrick, and again when he watches Shine kill Nathaniel Hinchcliffe.
Head of Limehouse K-Division, and thoroughly corrupt.
Affably Evil: He usually acts very friendly, and smiles most of the time.
Ambition Is Evil: The promotional material describes him as "A man obsessed by his own power and will. A will that has corrupted him and, if he has his way, will corrupt all and everything that falls within his reach."
Big Bad: Half the episodes of series 2 revolve around stopping him somehow. But he's actually also The Dragon to a Bigger Bad slumlord.