When Mary comes down to breakfast the first morning (after having dressed herself, possibly for the first time), her shoes are laced incorrectly, and her dress is buttoned wrong. When the camera changes angles an instant later, her dress and shoes are fastened correctly.
In the opening title sequence, when the door to the Secret Garden is unlocked, it opens inward from the right side. In the rest of the movie, the door opens inward from the left.
Elspeth Dudgeon (Susan Sowerby, Dickon's mother) was 78 years old. She, therefore, would have been well into her 60s when she gave birth to Dickon. However, this is not a Goof as actors frequently play characters of a different age than they are.
When Weatherstaff pops his head over the garden wall to let the children know that Colin's father is back, Dickon helps Colin back into his wheelchair. But as he does so, Stockwell (the actor portraying Colin) clearly uses his legs to assist in this task even though his character is a paraplegic.