After spending most of the episode as The Load, Fogg proves he has something to bring to the table by remembering an article about a man in Paris who's made a hot air balloon, including exactly where in the city to find him, thus giving the trio a way to escape the Gendarmerie who believe they were involved in an assassination plot against the President. The next episode reveals that he successfully flew it over the Alps despite never having flown a balloon before.
Abigail "Fix" Fortescue shows her Determinator status early. Your father printed your article under a male pseudonym? Fine, onto the next thing; follow his friend on his round-the-world adventure no one expects to work and write about that, without listening to anyone's Women Are Delicate crap or asking permission. The travellers you're following condescendingly try to send you home or tell you to Wait Here? Ignore them and just keep coming.
Episode 2:
Fogg confirms his status as The Smart Guy when the train is the wrong side of a dangerously-rickety bridge to get an injured child to a doctor in time. He uses his knowledge of science and technology to get the engine and one carriage across, stating that he can with such confidence that the boy's father, who previously looked down on Fogg as a dilettante, believes him enough to get firmly behind the plan.
Episode 3:
After being ditched by Fogg and Passpartout who decide the desert is no place for a woman, Abigail hires Jane Digby as a guide and sets out herself... saving their lives in the process.
When the party are being attacked by Bedouins who come at them in the dark, Fogg recognises a petroleum well and lights it on fire, allowing his companions to see who they're fighting.
Episode 4:
The morning after nearly dying of datura poisoning and with everyone else expecting him to forget about it, Fogg insists on continuing his efforts to intervene on behalf of a young man being court martialled for going AWOL to attend his wedding. He gave his word, dammit, poisoning or no poisoning.
Episode 5:
His actions may be misguided and the consequences terrible, but it must be admitted that Passpartout's theft of the White Dragon is some top-notch burglary. He secretes himself in the Governor's mansion during the garden party and waits until people are asleep, then searches the bedroom and steals the Dragon from around Lady Clemency's neck while she sleeps. Then he avoids the guards and sneaks out of the mansion his Triad acquaintance described as a "fortress," all without anyone getting a glimpse of him.
Fogg's behaviour while in prison. He's about to be flogged for a crime he didn't commit, knows he's being made to wait while another man is flogged within earshot to increase the torture through suspense and just simply refuses to give anyone the satisfaction of making him panic. The fact that a few tears do leak out while he's trying to distract himself with the paper, and his frantic body language when it appears he's going to be spared after all, show how scared he really is.
Episode 7:
Abigail's Big Damn Heroes moment as she rides to the menfolk's rescue into the saloon on a horse with guns blazing.
When Abigail's ammo runs out and she's about to be shot, Passpartout risks Taking the Bullet by diving on her. Bass Reeves was right; he did know when the time came.
Being the Defiant Captive as Kneedling holds a knife to his throat, intending to keep him from boarding the Henrietta. He stays calm and probes for information, when 70-odd days earlier he'd have been incoherent with panic.
Hits his Rage Breaking Point and holds his own in a fight with a street gang to the effect that they run away from him.
Stands up to Bellamy, exposing him for what he is to the Reform Club by making him choose between his honour and the money he needs to get out of debt. He chooses money, proving that he made the bet without having the means to cover it, and is chased out of the club.
Passpartout and Abigail stand up to a group of racist passengers who hassled them for being together by slow-dancing together in the most blatant way possible, leading to a very intense Held Gaze where they've clearly forgotten all about the Jerkasses they were trying to annoy.
