Brotherhood - S1-E7
Continuity mistake: When Nate and Brenda are hugging after they open the gift basket, Brenda's arms go instantly from around Nate's neck to down near his waist.
An Open Book - S1-E5
Continuity mistake: When Nate and Brenda are arguing, just after Brenda sits in the chair, we see from behind that her left hand which is holding a cigarette is held up by her face. The shot cuts to a view from in front and her hand is instantly in her lap.
Continuity mistake: When Brenda and her mother are at the restaurant, Brenda's cup moves from her left to her right hand instantly when the camera angle changes.
Continuity mistake: When Billy and Brenda are arguing in her apartment towards the start of the episode, the pendant on Brenda's necklace moves itself back and forth between shots.
Continuity mistake: When Brenda and Billy are arguing in the casino, the shoulder strap of Brenda's handbag moves from tucked under her collar in the close ups, to sitting halfway along her shoulder in the long shots.
Other mistake: Nate has his pager with him when sitting his exam paper. The pager goes off and he takes it from his pocket and reads a message without any comment from the exam invigilator.
Answer: Nate actually say "You can't take a picture of this, it's already gone." It's kinda hard to explain, but he's referring to the fact that the moment Claire wants to take a picture of is over already, and she can't take a photo of it, just a different, lesser moment.