Other mistake: Ok, this is being nitpicky, but in the scene where Freddy is pretending to be paralysed, and Lawrence (pretending to be a doctor) is whipping him on the legs in front of Janet to taunt him and get him to crack, in reality, Freddy's face would have been bright red from the pain. He could never hide that.
Continuity mistake: Right before Steve Martin and Michael Caine make their bet, Steve walks up to Michael sitting at a little white table. Every time the camera goes back to face Michael his handkerchief in the breast pocket of his jacket goes from sticking way out of his jacket, to barely visible.
Continuity mistake: Near the start of the movie, Marion arrives on the train to deflect Freddy away from Beaumont Sur Mer. In this scene there are four shots of her seated in the compartment. In the first three, her legs are crossed right over left, and in the fourth, left over right.
Visible crew/equipment: Upon seeing the dancers, when Freddy is rushed away in his wheelchair by Janet, the reflection of the boom operator chasing after them can be seen in the mirror on the wall that they are running along.
Continuity mistake: When Michael Caine and Steve Martin (as Ruprecht) are on the bed in Ruprecht's room, the swinging tire gains momentum and swings in a much larger arc without anyone touching it. It swings even more than when Michael Caine and his "fiancé" enter the room.
Answer: She pretends to be a clueless, naive "mark" for them to con. They initially think she is a rich, spoiled heiress (the kind of mark Lawrence usually exploits), and make a bet as to which of them can extort $50,000 from her first. Freddy poses as a veteran in need of $50,000 treatment; Lawrence poses as the psychologist who charges a fee of $50,000 to treat him (Freddy). They later "discover" that Janet is in fact a poor girl who won a contest to go to Europe. This turns them against one another, as Lawrence wants to cancel the bet, since he does not take advantage of people who cannot afford to lose the money he takes. Janet later tells Lawrence that Freddy stole the $50,000 she raised for his treatment, at which point Lawrence, disgusted by Freddy's behaviour and rich enough to make it right, gives her $50,000 of his own to cover her loss. After Lawrence sends Janet away, Freddy arrives and it is revealed that she never gave him $50,000, and trapped him until she could tell her story to Lawrence. Only then do they realise that she is, in fact, The Jackal (another con artist whose name has been dropped throughout the story, and who Lawrence initially believes is Freddy's alias), and she conned them both for $50,000.