Young Frank doesn't have a cleft chin. Teenage Frank does. In real life, Frank McCourt doesn't have a cleft chin.
When Frankie and his family are tearing down a wall to burn it, the picture of the pope is on the bed in one shot (at 1:34:03) before Frankie takes it off the wall and puts it on the bed (at 1:34:05).
A lunar eclipse can only occur when the moon is completely full. It would not cast a moving shadow.
During the lunar eclipse, the moon shown is actually a mirror image of the moon. In a later scene, showing clouds beginning to cover the moon, the moon is shown normally.
Frank uses the volume knob to change the station on his neighbor's radio (at 1:34:51).
When Frankie gets the beginnings of conjunctivitis, and he rolls his eyes back, the edges of his full-eye contacts are visible.
As Frankie McCourt bikes to the sanatorium to visit Theresa, a television antenna is visible on the roof of the building. RTE, the first Irish TV broadcaster, started transmission in 1961.
The Statue of Liberty has a solid, gold-plated flame, installed in 1984.
At the end of the film, a ship entering New York has radar. At the time, Radar was not available on commercial ships.
The newsreel shows German troops reoccupying the Rhineland in 1936. Frank was 10, so it was 1940, with WWII in progress and Germany occupying most of Europe.