Immediately before the storm, they are shown cruising on a fairly narrow river approaching a small island. During the storm, no land is visible and it appears the boat is in a far larger body of water. After the storm has cleared, they are shown on the island that was close by in the prior shots, and the river is narrow again.
The woman with the two children is within the range of a bear walking to the boat, yet she was unaffected by the extremely severe storm from the night before- her tent is up and none of her belongings are disturbed.
The "Chief" wears a uniform that says Sheriff's Department. As such, his title would be Sheriff, not Chief. A Chief is someone that heads up a local police department. Additionally, there is no law that requires a law enforcement agency in the State of Washington to wait a certain amount of time before taking a missing person report, for example this is clearly stated on the Seattle Police Department website. Given the severity of the storm, it would be a negligent act on his part not to search for people that he knew had been in that area coupled with the known threat of the bear.
Firing a round into the air is not something a trained law enforcement officer would do since the bullet could damage something or someone upon falling to earth. Additionally, in the circumstances shown it served absolutely no purpose- there was no one to signal.
The scene with the bear in the woods with Robert being pulled by Teresa and Christy is full of mistakes- the bear would have smelled them long before they had seen it, yet the bear was shown heading away from them. Then the bear is shown growling with no one around. Bears do not do so unless they are being threatened by something.
After the boat hits the rocks, Christy's breath can be seen when she is calling for her dad. In the following scenes, her breath is no longer visible, indicating the scenes were shot in two different temperatures.
Teresa works on the cell phones but never checks on or tries to use the marine radio on the boat.
Teresa, who is highly intelligent, and Christy, who is a teenager, never try to send a text via the cell phone.
The deputy says he put two tranquilizer darts into the bear, but the rifle he is carrying is not a tranquiler rifle- it is a regular center fire rifle as evidenced by his firing it twice.
The raft was in a bag that had not been damaged, yet when it is pulled out, it is shredded in some areas that were deep inside the bag. It is said it was damaged by the storm, but any damage to the inner portions would have been visible on the bag itself, as what ever caused the damage would have had to penetrate the bag.
In perhaps the largest plot hole of the movie, at the end the deputy does not shoot the bear. Teresa contrary to what the tracker said was not in his line of fire, she was off to one side. Then the bear attacked the tracker and the deputy just stood there. He could have literally touched the head of the bear with the muzzle of his rifle and killed it, but instead he allowed the tracker to be mauled and the bear to then run away.