Visible crew/equipment: While Barnum and Phillip sing "The Other Side" Phillip uses two stools to get up and down from the bar top. When he steps down from the bar top, in this wideshot (also the first shot of them in the pub and other shots) the two upright stools Phillip used are secured with additional support, note the floor area underneath the stools' legs have the same pattern as the rest of the floor, though we can see the outline where the pattern's lines don't match up. Additionally, we also see three actors' marks (in the shape of an "L") on the floor in front of the bar, which will be where Barnum and Phillip will stand when they agree on the ten percent. (00:36:05)
Continuity mistake: When Barnum goes to see Charity by the beach at the end of the film, they embrace. As the camera shows a close up of their faces Charity's head is on Barnum's right shoulder, but when they reverse the shot to show her expression she is now on his left shoulder. (01:30:10)
Revealing mistake: While Barnum and Phillip are singing "The Other Side" Phillip knocks over the first stool then steps on its side, and in this closeup we can see the extra two flat bars attached between the legs, for him to easily step on. We also see that the stool's seat is perfectly round in the closeup, but in previous and following shots, such as when Carlyle jumps off the bar then grabs his hat, one side of the seat has been cut to allow it to rest flat on the floor while on its side. Presumably, the closeup was digitally edited to make the seat appear round. (00:38:05)
Other mistake: When Jenny Lind is on stage singing 'Never Enough' during her American debut, she is in a very large theater with a crowded audience, and full orchestra. Obviously she would have to be miced, and have her voice amplified, for such a large space. When she is actually singing, her character's voice (or rather the dubbed voice of Loren Allred) is greatly amplified, with sound effects. But during this actual scene, there is no microphone or amplification system present. She does not have a microphone stand in front of her. There is no microphone hanging from the ceiling, or anywhere on stage that we can see. Technology was limited at that time, so she would not be using any type of cordless headset, or wireless microphone, which cannot be seen anyway. Her character's voice is obviously amplified a great deal through a microphone, which doesn't seem to exist.
Factual error: When they go to visit the Queen, the Union flag is being flown above Buckingham Palace. The Union flag is only flown when the Queen is not in residence. As the Queen is in residence, the 'Royal Standard' flag should be flown. And anyway, the Union flag has only been flown at the palace since the death of Princess Diana in 1997. (00:43:00)
Continuity mistake: When Charity's father slaps young Barnum for making her laugh he is wearing the partially tailored suit. Then he walks past him an instant later and he is not wearing it.
Audio problem: During "This is me", when they enter the room and get to the "oooh oh oh" part if you watch the albino the sync is out as their mouths open after the music has ended on that part.