I was just reading, and came up on the part where arya is with the brotherhood, and hears the Karstarks are near looking for Jaime. She thinks if she gets the chance she wants to escape and join up with them.
This is like days after Robb executed their lord, if Arya had acted on that, which would have been a good idea the previous week, well they would have either executed her, or held her hostage at the least.
Im sure there are tons more of little moments like this, where day old information, or a tiny miscalculation could have ended really badly. Im talking about the smaller near misses, that just made you go "oh jeeze, that would have turned out badly."