When calling out "legs 11" during the bingo game she holds a blue ball but a back shot shows her holding a white ball and in the next front shot she has the original blue ball again. As an extra the white ball is not 11 but 69 (which maybe a playful joke with the crew and cast)
When Amelia is screaming at the Babadook after the picture on the dresser falls over, the black frame on the wall to the left of her head is noticeably slanted, but when she is shown again the frame is perfectly straight. When Amelia says "You're trespassing in my house!" the same frame falls. A few seconds later, when she is shown again, it is back on the wall. Then right after they show Sam hugging Amelia from behind the frame is gone again.
When Amelia gets the ripped up book back and looks at the new pages, the last page says (Line 3): the more you deny the (Line 4): stronger I get. Yet when the camera pans over the words on the page, the second 'the' has been cut out from the end of line three and moved to the fourth line making it (Line 4): the stronger I get.
After reading The Babadook and putting Samuel to bed, Amelia watches TV and sees a commercial for phone sex. The number is 1-900-646-EASY, which would be a US telephone number, even though the film is set in Australia.