After Paddy dies, and the children pack up the dinghy, the handmade toy boat is prominently displayed on top of their belongings. Years later, when they return to the original hut, Richard is digging through the rubble and finds what is left of the toy boat that he clearly took with him.
When Emmeline is teaching the baby how to swim, she calls Richard down to watch. When Em is holding the baby, you can hear a child laughing that doesn't match any of the actors. Later, you hear the toddler Paddy laugh and it sounds identical to the laugh heard before.
When Emmeline walks in the water she accidentally steps on a fish and gets sick. The fish that the movie shows is called Stone Fish and in fact if you step on one the venom will cause excruciating pain and also shock, paralysis, tissue death and if not treated within few hours also death. Emmeline doesn't seem to suffer from any of these symptoms and it seems it takes some time until Richard finds her.
Richard and Emmeline have both come of age on an island away from civilization. Both are clean shaven, however. While a teenage boy may not sprout a full beard Richard should at least show growing sideburns and some peach-fuzz on the chin. He even references that he is growing "all these hairs" on his body. Likewise, Emmeline's armpits should be hirsute. How did they learn to shave and where did they get razors?
When Paddy and the kids first sight land and begin to sail toward it, the mountainous coastline of a large land mass can faintly be seen behind them, indicating that the island is not as remote as we are led to believe.
When Richard goes fishing from the boat and his catch is attacked by sharks, tearing the line from his hands, a rope can clearly be seen dragging the first (presumably dead/fake) shark through the water