Revealing mistake: Mr Hyde makes no bubbles when growling underwater. (01:11:30)
Revealing mistake: In the mountain scene where the League is staking out the fortress from a very cold cave, there is no breath to be seen. (01:16:25)
Revealing mistake: When Skinner is walking around in the snow, after he says he's standing outside completely naked, he should have been leaving footprints in the snow. When he does, between shots, they're practically floating. (01:20:55)
Revealing mistake: In the scene early on in the movie where Quatermain fights the goons in the bar, it is quite easy to notice when it is Sean Connery, and when it is his stunt double.
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.
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)
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)
Revealing mistake: The Germans in the movie, good ones as well as evil ones, speak German with more or less strange accents. (00:03:20 - 00:04:10)
Revealing mistake: Just before the Britannia Club blows up, Sanderson Reed steps through the poisoned guy's wrist.
Revealing mistake: When the Nautilus' hull is breached by the explosives Gray has set, water rushes in with great force. The crewmen who get hit by the water do not get swept off their feet - as they should have - but instead keep on running. (01:07:10)
Answer: I haven't read this book of Wilde, but I think alterations were prompted not by copyright issues but because this conveniences the "league" storyline.