Goofs

Young Tolkien has dark hazel eyes, but the adult Tolkien has clear blue eyes.

One of Tolkien's friends sports a moustache during the war and is mocked for it. Actually, moustaches were mandatory in the British military at the start of World War I. Tolkien himself wore a moustache during his service.

Tolkien's mother took them to Birmingham when he was 3, not the age he is in the beginning, and he lived in or about Birmingham all though his schooling years.

In real life J.R.R. Tolkien did not stand a full head taller than his wife. They were about the same height. (Nicholas Hoult is far too tall.)

The priest uses the term "home-schooled" but Webster's dictionary says this term was first used in 1980.

When it is announced that war has broken out, the speaker says it is because Germany had invaded Belgium. That had been front page news and surely the most talked about topic everywhere for a day. He more likely would have said that Germany had ignored the ultimatum to leave Belgium.

Tolkien gives Edith a flyer for a concert at Birmingham Symphony Hall of Richard Wagner's Tetralogy "The Ring Cycle" given by the Birmingham Symphony Orchestra and Chorus. Symphony Hall was opened in 1991. Before that, orchestral concerts were given at Birmingham Town Hall. While the name of the Birmingham Orchestra is correct for the period, it did not have a chorus until 1973. The venue that they then go to in the film is not a concert hall, but an opera house, so it's unlikely that a symphony orchestra would have given the concert in that venue, since it would have been a full performance. Still, at least they didn't call it a quadrilogy, eh?

The professor uses the discredited translation of "foolhardy" for Tolkien's last name. Actually the Tolkien name means "son/descendant of Tolk", although Tolkien himself believed the former throughout his life.