Near the end, when Claire is about to let the bird go, Charlie had already placed the message on it, but it is still visible in his hand.
When Charlie is reading the note Claire is sending with the seagull, he is seen folding the paper at around 38:20. The camera cuts to a close up of Charlie and Claire, he then folds the paper again.
When Claire follows Desmond and he catches the bird, his right shirt sleeve changes positions between shots (at around 33:30). As he reaches out to pick up the bird, his right sleeve is fully extended. When he turns to show the bird to Claire, the sleeve is up above his elbow.
When Claire's mother is on life support in the hospital, her aunt says they cannot afford it. But in Australia Medicare will cover the cost.
Just after John drops to the ground from crossing the fence, there is a shot of Kate examining Mikhail's body. He is very obviously breathing.
The police officer interviewing Claire after her car crash introduced himself as Officer Barnes. Australian police refer to themselves by their ranks, so he would have said that he was Constable Barnes. The same error appears in the credits.