Audio problem: As soon as Nemo begins playing the record, we hear a woman say "Ready, professor?". However, the actual recording doesn't start until the needle is put into position, which is after she says that.
Plot hole: What on earth are those sailors doing with Hyde when he is chained up on The Nautilus? He is solidly chained to the floor and walls and they keep stepping up to him to allow him to swat them out of the way, risking injury or even death. They stand around like idiots as if waiting their turn to walk up to Hyde and be belted across the room. Why? Why are they even there? Hyde doesn't need subduing, and if he needed guarding they could do it without getting into range.
Suggested correction: They are there to subdue him because he is strong enough to tear the chains from the walls, which he does seconds after they stop trying.
Plot hole: When the team plays back the record, it contains an extremely high-pitched tone which triggers the crystal sensors on the ship. But the speech on the record is low quality. This low quality would be the result of extreme frequencies being lost; but if they were, the trigger tone (a VERY extreme frequency) would be lost too. If the League's gramophones are capable of recording and playing such a tone, they should also be able to record and play back the speech without any quality loss. (01:09:05)
Continuity mistake: When Mina bites the attacker at Dorian Gray's house for the first time there's blood all over her face, but after she bites him the second time it's gone before she had a chance to wipe it off (even that wouldn't have removed the blood so completely). (00:28:25)
Suggested correction: We don't see what she does when she's down though. Whilst you are correct you could be forgiven for believing that she may give word her face on his clothing.
Visible crew/equipment: In the shot where Quatermain shoots at three of the attackers they are attached to wires you see running across the floor, probably needed to trigger off the sparks from their steel armor. (00:09:00)
Continuity mistake: When Quatermain realizes that Skinner is in his room (on the Nautilus), he puts out the lamp and the room goes black. We hear a scuffle and then the door opens and lights the room and we see Quatermain throwing the invisible Skinner out the door. But when Quatermain shuts the door, the room does not go dark again. (00:39:50)
Factual error: When M tells Allan Quatermain that he and his team have four days to go from London to Venice, he answers that this is impossible, and captain Nemo replies that it will be possible thanks to his science-fictional devices. Actually, on late 19th century railways, this trip would have taken less than two days. For example, the Peninsular Express departed every Friday afternoon from London, and it arrived at Brindisi, a considerably more distant town in southern Italy, on Sunday afternoon. (00:16:39)
Factual error: Apparently, Captain Nemo's submarine, Nautilus, is a shape-shifter. When it first surfaces next to the dock, it appears to rise easily 100 feet above the water, and that's only the visible part of the submarine; the bulk of the craft is still below the surface. This suggests that the water is a good 300 feet deep or more right off the dock, which is impossible. At this enormous size, it's also impossible that the Nautilus negotiates inland waterways, as when she goes to Mongolia. Strangely, we also see an overhead shot in which the Nautilus appears to rise only about 40 feet above the surface (compared to three-storey buildings directly adjacent).
Revealing mistake: In several scenes where Skinner is shown with his full outfit and makeup, you can see skin through the makeup. No skin should be noticeable on an invisible man. This is especially noticeable on his ears.
Continuity mistake: When the team sees the Nautilus for the first time, rising from the Thames, the water around it is churned into large waves. But in the shots looking down on the team on the dock, you can see that the water is calm and still. (00:32:50)
Other mistake: When Allan is teaching Sawyer to shoot, he says that he 'brought his son along' on a mission. However, the subtitles say 'son-in-law'. (00:44:35)
Revealing mistake: In the scene where Allan Quatermain is waiting for Skinner in the snow and the white tiger shows up, when the camera shows a close-up of Allan, there is snow inside his goggles on his head. If it is snowing hard and the snow inside his goggles isn't adding up, it should have been melting or been melted. But it doesn't change at all, which proves it to be fake snow. How did it get in there anyway? (01:17:15)
Plot hole: When we are shown the Nautilus' journey into Mongolia, are we expected to believe that this very, very long ship could travel down this river, even though it has a lot of sharp turns in it? (01:15:10)
Other mistake: Before Quatermain shoots the fourth attacker long distance he puts on his glasses, cursing his getting old. However, when he aims he looks over the rim. (00:11:05)
Deliberate mistake: After Mina leaves the car in Venice, Sawyer just manages to avoid several obstacles on the way, including a bend in the canal. But in the first scene, where Sawyer swerves the car around, its front should have slipped into the water anyway, considering the speed of the car and the tightness of the street, which makes a sharp L-turn at such close quarters next to impossible. But then the scene jump-cuts, and the car is well past the hazard.
Plot hole: As the Nautilus makes its way along a canal in Venice, you can see a bridge ahead of it that is far too low for the sub to pass under. Yet without altering its running depth, the sub miraculously appears in the canal well beyond this bridge moments later, and that bridge is not damaged.
Factual error: Quatermain sits in the snow for hours, without gloves, holding a rifle with substantial metal parts, yet his hands don't freeze onto it or (presumably) get frostbitten. (01:16:55)
Continuity mistake: In the beginning when the tank is seen coming it breaks down the same gate twice. (00:01:25)
Continuity mistake: When Dorian is getting shot, the shooter's mask thing falls down. About two shots later it is back up, in the next shot it is down again. (00:26:45)
Revealing mistake: In the bit where Mina is using her scientific equipment and Dorian gives her a drink, the blood is on her hand before she cuts herself. (00:47:55)