Trivia: When the sheriff tears Daniel Craig's wanted poster off the wall in the jail, underneath there's a wanted poster with a photo of a mustached Jon Favreau (the Director).
Continuity mistake: Earlier in the film when they come across Hunt and the other bandits, Hunt gets hit in the face and has one of his front teeth chipped and broken. But later in the film before they attack the alien stronghold when he's talking, his teeth are perfect.
Character mistake: When the posse is heading out in the morning, one guy says that it's heading north and they start riding in the direction he's pointing. However it's supposed to be first thing in the morning, and you can see the shadows of the horses cast to the left of screen while they are riding towards the camera. The sun rises in the east, which would be right of screen with the shadows cast towards the west. Since they are riding towards camera, this puts them heading south.
Answer: Don't recall seeing Liev, as for your second question, maybe Hunt figured it was nothing Jake didn't already know, or at least conclude.