Haakon's footwear repairs itself as he spends time on the island. When he's washed ashore, he's barefoot, or nearly so, and when he falls into the pit he has just part of a shoe on his right foot. Then, as he builds the boobytraps, he has parts of shoes on both feet. He sees the flare from the other island, builds a boat and launches it barefoot - then wades out of the water on the other island wearing two completely intact shoes.
In the climax, Merrick's boat is blown to bits. Yet, the caliber and type of the cannon Mary uses are inconsistent with the blast it creates, not to mention projectiles of the time did not explode on impact.
Among the debris washed ashore after the shipwreck is an anchor.
When Merrick shoots the chain on the ship, the chain breaks before his gun fires.
When Haakon drops a crate with explosives in it onto a bonfire, it blows up before it reaches the bonfire.
During the climactic chase scene, it is obvious that the cannon Mary fires is a lightweight prop.
While the movie is set in the 1850's, there are several anachronisms in the uniforms and ships (too new, most likely from the 1890's), weapons (too old, around 1800's) and the major plot of pirates themselves, that had stopped being an issue by time.
Gorillas don't exist in the Pacific Ocean.