When Amy is putting the baby to sleep before they all end up in the water, the baby has almost no hair. When the camera cuts to the sleeping baby, she has a full head of curly hair. It's clearly not the same baby.
The second time you see the baby asleep on the boat, it suddenly has a dummy in its mouth. The third time, it is gone again.
At 1hr 2min 30 seconds into the film, a female character is floating face-up in the water. In the context of the story, she is supposed to be entirely nude. However, the camera inadvertently shows the skin-colored modesty patch that the actress is using to cover her right nipple.
No authentic American Flag of that size would rip that easily.
Lauren stands at the front of the boat to imitate Rose from Titanic. She has Zach place his hand on her stomach but in the next shot, his hand is on his side.
At about 1:03:36, you can see the shadow of the camera on the boat.
The characters are not trying to grab the anchor at the bow, although it is closer to the waterline than the deck edge at the port side which they are trying to reach.