Continuity mistake: When Michael Collins searches through the files in the castle he takes the only photograph from his file and shows it later to Harry Boland. But when the file is given to Soames, the photograph is back in. (00:30:30 - 00:52:15)
Suggested correction: The British authorities in Dublin Castle were capable of making copies of photographs and reproducing them. They would not have had only one copy.
Other mistake: After the attack on the police station we see a train passing by in front of the fire. The shiny train reflects the flames in a way that could only be caused by another fire for which there is no evidence. (00:16:20)
Suggested correction: We do not know that the IRA didn't set another fire. They may well have, but it wasn't shown. As there is another fire reflected on the train, then it must have been set, but the viewer was not shown the details.
Continuity mistake: When Michael Collins and his men raid the police station they throw torches on the roof. A second later the whole building is on fire, and the policemen run out coughing and gasping for air. However, when the IRA people go in to get the police guns the air is quite breathable. (00:15:25)
Suggested correction: When the policemen exited the building, they opened the doors, which let much of the smoke out, allowing the IRA men to enter without succumbing to smoke inhalation.