Continuity mistake: There is a shot of the beans in Jack's hand when the monk gives them to him. There are a total of 8 beans. Later, one of the beans goes under the floorboards of Jack's house and that turns into a beanstalk, bringing the bean count down to 7. After climbing the beanstalk, Roderick forces Jack to give him the beans. Jack keeps one of the beans bringing the bean count down to 6. No more beans are used after this until the giants use the beans as a way down to Earth. But when the lead giant takes the beans out of the bag, there are now only 5 beans.
Continuity mistake: During the giant siege on the English castle, the giants use grappling hooks to pull the drawbridge open as the human defenders inside struggle to pull the drawbridge closed with an enormous hand-winch. The giants overpower the humans, and the huge hand-winch is actually torn loose of its moorings and tumbles away, useless. The humans then scramble to use "scorpion" tow lines to close the drawbridge. As the order is given to man the tow lines, the camera briefly cuts to the drawbridge entrance, where we again see the enormous hand-winch, still on its moorings, quite intact and fully functional.
Continuity mistake: When the humans and giants are pulling the ropes to open and close the gate, the hooks of the big guys disappear in one moment of the struggle.