(at around 45 mins) When Helen Grace is at her job just before she notices her children outside, she is being told by her coworker what to push on the keyboard. She clearly is pushing random keys and not the ones spoken.
(at around 42 mins) On the way out to see Aunt Lucinda, Simon calls to Mullory and gives her an ocular device he has found that holds the seeing stone. Just before leaving the house, Mullory is seen putting the ocular device over her right eye. When Mullory and Jared first enter the tunnel, the ocular device is on the right eye as seen earlier. However, a few moments later while running through the tunnel the ocular device is on the left eye. As the two approach an intersection the ocular device is back on the right eye.
(at around 1h 14 mins) While fighting the goblins in their house, Helen (Jared, Mallory, and Simon's mother) does not have the sight. Half way through the fighting, the seeing stone disappears from her face, yet she can still see all of the creatures and continue fighting.
(at around 1h 13 mins) During the fight scene in the house, Jared throws several tomato bombs at the invaders. He is shown having only 1 in his hand throughout the scene. But when he throws the bomb a new one appears in his hand.
Simon tells Arthur Spiderwick that Arthur is his (Simon's) great-great uncle, but that is incorrect. If Lucinda is Simon's great aunt, then Arthur would be Simon's great-grandfather. If, on the other hand, Arthur is Simon's great-great uncle, then Lucinda would be Simon's first cousin twice-removed.
The goof item below may give away important plot points.
(at around 56 mins) After Jared and Mallory visit Lucinda, back at the house when Mallory takes Jared outside to show that the goblins are gone, she is not using the seeing stone. Then she reacts when Hogsqueal approaches as if she can see him but in the next shot she acts like she can't see him.