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.
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.
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.