Continuity mistake: The red ink/marker encircling "notstop looking" is a continuous line forming an oval; the two ends meet above the "s" in notstop. The second time Oskar looks at it, the oval is different - two slightly overlapping ovals above the "t" in stop and the ends do not meet. The oval also stays mostly on the same line whereas the first one was wider, going into the words on the lines above and below. Also, the red ink does NOT look like it bled through the page, though that's what Oskar figures out. (00:05:13 - 00:14:00)
Other mistake: When Oscar finds the business card under the swing, the narration doesn't match the writing on the flip side of the card.