Historically Incorrect

I thought this film was brilliant and after watching it I decided to look further into the Mutiny on the Bounty. I've been reading the book on which the film is based 'Captain Bligh and Mr. Christian' and discovered that part of this film is historically incorrect.
In the film, when the ship leaves Tahiti Bligh announces the they'll sail around the Cape Horn. The men’s reaction is to say "you've gone mad, you'll kill us all!". The film then uses this as one of the reasons when the men mutinied.
However in reality this never happened, after leaving Tahiti the Bounty sailed west towards the Indian Ocean.

Also at the end of the film it says some believe Fletcher Christian died on the Pitcairn Island and others that he returned to England. When the fact is it's been clearly documented that he was murdered on Pitcairn Island by one of the Tahitian men, this took place in 1793. Christian was shot in the head, his last words were "Oh, dear" and then he was butchered with an axe.