Flycatcher having been "let go" by Ichabod Crane and getting a job for the Tweedles instead.Were this true in the game, Bigby would have known immediately that Snow wasn't dead.
It's also revealed in the comics that his connection to Snow White is so powerful, he knows exactly where she is and what she's feeling at every point in time by her musk alone. The majority of these moments of tension wouldn't last for more than a few minutes if his sense of smell was as powerful as it is in the comics, and if it was even as strong as a normal dog or wolf, the chase scenes would be much less "which way did they go"-ish. A lot of points in the game rely on things being a surprise to the player, and by extension Bigby himself. In the comics, it is revealed that Bigby's sense of smell is so powerful, he has to chain smoke to dull his senses and make things bearable. It's assumed Dum is as well, being, well, twins. Acrofatic: Tweedle Dee, in spades, during his foot chase with Bigby.
Accidental Hero: As the Woodsman confesses, he went to Grandmother's House attempting to rob her and Red Riding Hood, only to find Bigby already there and end up being lauded as a hero for cutting the pair out.That scene never appears in the actual episode, Bigby never brings the possibility up, and the purpose of the murders was to cover up a conspiracy.