Captain Aubrey rejects sailing into the "rain forest" of Brazil for a new mast (at around 23 mins). The word "rain forest" was brought into English by a literal translation of the German word "regenwald" from a book written in 1898 and translated into English in 1903.
When Hollom has a panic attack after being menaced by the crew, Midshipman Blakeney asks (at around 1h 20 mins) "Are you O.K. Mr. Hollom?" Although the movie is set in 1805, according to the Webster New World Dictionary of the American Language (second college edition) "O.K." is an American colloquialism which was first used March 23, 1839 by C.G. Greene in the Boston Morning Post (Webster New World Dictionary of the American Language (second college edition) p. 989.)
In the closing scenes, as the dead are buried at sea, the crew is saying the Lord's Prayer (at around 2h 00 mins). Given the year, they would be using the version known by all from The Book of Common Prayer (1662 edition): "Our Father, which art in heaven..." Instead they say, "Our Father, who art in heaven..." the first instance of which actually appeared in the American Book of Common Prayer (1892 Revision). As a ship of the King's Navy, the established Anglican Book of Common Prayer would be the normative source of liturgy and prayer.
During the cricket match on the Galapagos, the bowler is shown delivering the ball overarm (at around 1h 30 mins). A technique that was illegal under the laws of cricket until 1864, in 1805 only underarm bowling was deemed legal.
The silverware used at the Captain's table and during the brain surgery scene (spoon at 00:24:11) is machine made and of a style that would not have been used till after the late 1830s when techniques for smithing changed. Spoons of that era would likely not be molded in one piece.
Throughout the fighting, pistols are seen to function well. During this time period, flintlock pistols failed to discharge up to 50% of the time, and were considered a secondary weapon in close combat.
Some of the signal flags hanging from Surprise when under the sun didn't exist in the Napoleonic era. They would seem to spell Surprise as there are the same number of flags as letters in Surprise, but they don't actually spell or signal anything.
Following the first encounter with the Acheron, Captain Aubrey inspects a chart using a magnifier. In the magnified image, a pattern of ink overspray is visible surrounding each letter in the phrase "Hidden Reef" as the magnifier is panned over it (at around 18 mins). Such a pattern is precisely characteristic of modern-day inkjet printers, but of neither quill pens or the printing presses of the period.
During the final scene when Aubrey and Maturin are playing their instruments together, Aubrey briefly stops strumming his violin to put it to his neck. A violin can still be heard strumming (at around 2h 07 mins) as he does this, even though Maturin has stopped playing his cello with his bow and is also strumming at a lower key.
The two insects referred to as 'weevils' at the Captain's Mess table (at around 34 mins) were most certainly not weevils. The insects historically referred to as 'biscuit weevils', at the time, were extremely small and would not have shown up on camera therefore some artistic licence was taken to make the scene work.
When Captain Aubrey orders the Surprise due South after battling around the horn, Lieutenant Pullings says, "Due South, Mr Bonden," to Barrett Bonden, who is at the wheel. The prefix "Mr" was used only for officers and would not have been used to refer to Bonden, who was the captain's coxswain and so not an officer.
Dr. Stephen Maturin observes the Galápagos marine iguana and later captures specimens of various local flora and fauna. The iguana he captures and then releases later on are green iguana, one of the most common types of iguana, a land animal that isn't found on the the Galápagos islands. This can be explained by the fact that marine iguana are a rare species, while many green iguana live in captivity and as pets.
When the ship is about to leave the Galapagos, Dr Maturin is on deck and has a growth of beard/moustache. He goes down to the cabin to remonstrate with Aubrey but appears there clean shaven. On deck again, slightly later, he has re-acquired his stubble.
In the opening scene when Surprise is attacked by Acheron, Captain Aubrey gives to command to "run out the starboard battery" (at around 28 mins). We then cut to the gun deck showing the guns not yet run out (at around 38 mins). However, Calamy ordered beat-to-quarters at 06:20 and while the boats were being lowered at 08:18 the port guns can be seen already run out and in a long shot from the stern at 08:24 the starboard guns appear to have been run out as well.
Prior to the first encounter with the Acheron we see the watch glass turned and eight bells struck (at around 3 mins). A few moments later (at around 26 mins), we see the glass turned again and six bells is struck which would mean that three hours had passed, yet the ship is still clearing for action - something which would have taken ten to fifteen minutes.
When Maturin is wounded, the bullet is removed from his left side (at around 1h 30 mins). However, when he and Aubrey are discussing the length of their stay at the Galapagos, he is holding his right side and using a cane on that side as well (at around 1h 35 mins).
When Aubrey decides to follow the Acheron into Valpariso, he order's the crew beat to quarters (at around 2h 06 mins). As a result, we see crew members and Royal Marines climbing the rigging into their assigned places on the mast (actually, repeated shots from beat-to-quarters responses from earlier scenes). However, in the overhead shot of the Rose/Surprise, there are clearly no men positioned anywhere above the deck (at around 2h 07 mins).
During the Storm when the Surprise is chasing the Acheron around Cape Horn, Barrett Bonden is shown alone at the wheel. It was customary on a Royal Navy vessel of the time to always have at least two men at the wheel both as a security measure in case one man was injured in battle, and because the rudder itself was extremely heavy and difficult to turn. During any sort of heavy weather there would certainly have been four or more men at the wheel as one man would not be able to control the rudder (which is why the ship has two connected wheels).
As the "Surprise" sails around the Horn and the weather deteriorates, the ship begins to ice up. However, in one shot the icicles on the bow of the ship are hanging straight down (at around 57 mins), which could not happen unless the "Surprise" was becalmed.
Just after the beginning of the movie we see and hear eight bells being struck (at around 3 mins). This signals the end of a watch, however, it is clear from the scenes below decks that the watch is not actually being changed.
At the beginning of the movie Surprise is shown with a white pennant, indicating she was under independent command; however, during the final fight with the Acheron the Surprise flies a Red Ensign. She should have been flying a White Ensign.
The Acheron is supposed to be a 44-gun frigate built in America and sold to a French privateer. No large American-built warship was sold to any foreign concern (nation or individual) during this time period (except the 74-gun ship-of-the-line "America" given to France after the Revolutionary War). American-built warships did not have a good reputation in Europe (something reinforced by the poorly built "America"). It was not until the War of 1812 that the large American frigates proved the superiority of their design. The use of a large American-built frigate in the story is apparently a holdover from the book in which it is an American warship which is pursued.
Throughout the movie, Captain Howard of the Royal Marines is referred to as "Captain Howard". British Naval Tradition would have dictated that he would have been given a "courtesy promotion" to Major. This "courtesy promotion" would not have been a permanent promotion, but rather just a change in wording to avoid confusion between the ship's captain and the Marine captain.
At the beginning of the movie, Midshipman Calamy issues the order to "beat to quarters". This would not have been ordered by a midshipman. He would have reported to the officer of the watch (one of the lieutenants or the Master, certainly not another midshipman, as was shown) who would then have woken the Captain and reported that a sail had been spotted. It would then be up to the Captain to give the order.
In many scenes HMS Surprise/HMS Rose is clearly motoring, as the sails are either hanging limp or aback. In one scene the ship seems to be making at least 5 knots with all sails backed (at around 1h 12 mins).
Dr. Maturin presents Captain Aubrey a "stick insect" (order Phasmatodea) collected on the Galapagos. No species of Phasmatodea has ever been recorded as native to the Galapagos or otherwise established there.
During the first encounter with Acheron, the order is given to beat to quarters, but during the first scenes when Mr. Calamy is searching the fog with his glass, the gun ports are open and the guns have been run out. This indicates that Surprise was already at quarters.
As two seamen enter Aubry's cabin to present him with a model of the "phantom's" hull, both salute the captain (at around 28 mins). However, one salutes with his left hand while the other salutes with his right. It is often assumed that a proper salute is completed with the right hand. The salute was not standardized in the Royal Navy until the late Nineteenth Century. Before that enlisted "saluted" by "tugging the forelock". While typically done with the right hand, this form of "salute" could be performed with either hand.
Mr. Blakeney has his right arm amputated after the first encounter with the Acheron, but later when Captain Aubrey is teaching the midshipmen how to work their sextants to determine noon, it appears that Mr. Blakeney still has both hands on his sextant (at around 38 mins). However, Captain Aubrey is assisting the midshipman by holding the sextant upright while Blakeney makes adjustments.
After the doctor has been shot, we see him in the hammock being tended to. He is very pale. However, as the hammock shifts, you can see the makeup line just below his neck while the rest of his upper body is still normal color (At 01:29:03 to 01:29:06).
When the crew is shown battling a leak below the waterline, the boat is pitching on the sea. However the water is not sloshing back and forth in the bilge/hold because the "pitching" of the boat is simulated by camera movement.
At about 65 minutes in, while in the Galapagos island, when the Surprise picks up the sailors from the Albatros from the small life boat, Captain Aubrey orders "food and water for these men." While the Captain of the Albatros is telling his story, the camera pans to the right, and targets a sailor who is drinking from a cup. When the cup is raised to his mouth, one can clearly see his lips are firmly closed.
The goof items below may give away important plot points.
During the boarding, Mr. Higgins prevents a cannon being fired by stopping the flintlock mechanism. Flintlocks, or gunlocks, on cannon were first used by the Royal Navy in 1745, but they were a rarity on French ships at this time who still used the matchlock, or linstock, to fire their cannon.
When Lieutenant Pullings is given command of the captured Acheron, he is hailed as "Captain" before leaving the Surprise (at around 2h 04 mins). Such an officer would be the "prize master" of that vessel and referenced by his rank. Within the Royal Navy the title of "captain" was only applied to an officer, regardless of rank, who was assigned as the commander of a commissioned vessel (which a prize ship was not).
When the Surprise, while disguised as a whaling ship, is being chased by the Acheron, the smoke from the Surprise is trailing behind her (at around 1h 45 mins). That would only be possible if the wind was coming from dead ahead, which is impossible in a sailing vessel.
To pretend to be a whaling ship, Surprise removes its topgallant masts, apparently to change its appearance. Drawing and paintings of whaling ships show them to have been rigged in the same manner as any ships of their era; that is, with main, top, and topgallant masts. Thus there is no reason for the modification shown, and it would be far more likely to make the Acheron cautious because of the odd modified appearance of the Surprise.