Revealing mistake: The oil lamp carried by Mary when she first finds Colin has a flame that never flickers, and is likely an electric lamp.
Visible crew/equipment: During the scene where Mary is crying with her face at the bushes and Dickon walks in to try to cheer her up, if you keep your eyes at the top of the screen just as Dickon walks closer to her, you can see for a second the microphone being pulled up, which looks like a black object right in between the two walls of the bush. (01:30:15)
Factual error: The footage of the garden blooming in the spring includes a shot of a monarch butterfly emerging from a cocoon. The monarch is very rare in England, usually found in the southwest; so this footage is more likely from North or Central America where the insects are commonplace.
Deliberate mistake: In the scene where Mary (Kate Maberly) emerges from the bath tub she glances uneasily at the camera for a brief second. (00:56:00)
Visible crew/equipment: At the beginning of the film when the man calls out Mary's name through the speakerphone you can see a clear reflection of set lighting in his glasses. (00:05:54)
Answer: Mary is told by Dickon that Colin was born early, and Martha even says that he was born very small and weak and no-one thought that he would survive. I think his premature birth made them believe that he was going to be a sickly child.