The Harry Potter series
The protagonist's scar emerged and vanished miraculously in the popular movies.
The Lord of the Rings
Legolas, the elf in the fabled trilogy, has different colored eyes in each scene. The color contact lenses must have slipped the makeup artists' minds.
Forrest Gump
The movie's storyline states that Forrest purchased stock in a well-known corporation in 1975, although in actuality, those shares weren't accessible until 1981.