The Alcoholic: Monty is definitely a problem drinker, and he shows signs of having developed a dependency on alcohol at several points throughout the novel. He often reaches for spirits to numb his feelings at times of emotional turmoil (which come up pretty frequently...)
Beauty Is Never Tarnished: Somewhat inverted - when Monty is shot by the Duke of Bourbon, he loses his right ear and sustains some scarring on the right side of his face. However, all his facial features and most of the rest of his face are undamaged - he even jokes that his prized dimples remain very much intact.
Dark and Troubled Past: Like his sister Felicity, for the first few chapters readers are unaware of the extent of his father's physical abuse, or the degree to which it sparked Monty's psychological downward spiral.
It's All About Me: Monty's actions towards the beginning would have you believing this. He's a partying narcissist who wants to be in a relationship with Percy, and is sometimes resentful towards Percy when he apparently fails to reciprocate his feelings.
The Versailles incident really highlights his lack of perspective when he fails to realize that if either Percy or Felicity had been in the same situation, they would be either disowned, imprisoned, or killed.
Trauma Button: When someone - usually another man - reaches their arm towards him suddenly, Monty often reflexively raises his hands in front of his face. Especially when the person is his father, whose beatings are the reason Monty experiences this post-traumatic reaction.
Ambiguously Gay: At first. From the beginning, Monty's narration certainly implies that he's always thought there was a chance that he and Percy might one day sleep together, even if he doesn't think Percy returns his romantic feelings. Bearing in mind, we later find out that before their kiss at the music hall Monty has never discussed Percy's sexuality with him, or seen him be overt about an attraction to anyone.
Chocolate Baby: Percy is a mixed race, bastard son who, despite the racist hierarchy of the time and place, is raised as a lord by his late father's relatives.
Dark Secret: Percy isn't going to study law in Holland after the Tour. His aunt and uncle are banishing him to a sanitorium (read: asylum) because they are ashamed of the fact he has epilepsy, a condition which was very poorly understood at the time.
Disabled Love Interest: Percy has epilepsy, which he has been hiding from Monty for two years. Percy doesn't believe that he should need to be 'cured' in order to be able to live the life he wants to live, and wishes his relatives (and to a lesser extent Monty, who comes around) would accept that.