When the King first visits More's house, we see a yellow Labrador Retriever running to the house. However, the dog with the specific physical characteristics that we associate Labradors with today (and that was shown), wasn't bred yet.
Wolsey says it is known that Catherine (of Aragon) was barren, or infertile. In fact by this point she had given birth several times, including to the future Mary Tudor, Queen of England, though there were no other surviving children.
When King Henry visits Thomas More's house and steps off the boat, he steps into mud and makes light of it. When his retinue follow, it is seen their feet and leggings are already muddy from a previous take.
When Thomas More is imprisoned in the Tower of London, he looks out the window of his cell, which is shown to have bars. When the camera switches to a close-up of the window and its view of the outside, the window no longer has any bars.
In the opening scene, when Wolsey is sealing the letter to More with wax and his official seal, after he hands the letter to Cromwell and he folds it and pours the sealing wax, there is a string of wax that trails from the ladle and over the letter. Yet in the closeup when Wolsey is applying his official seal, that trail of wax is gone, and the letter is clear of any dripped wax. Also, it's obvious that the long shot and the closeup of Wolsey applying the seal are separate takes: the blob of wax in the long shot is smaller than that in the closeup, and the letter is folded differently (there's more of an overlap in the folded letter in the closeup).
When Henry says curtly that it is 8 o'clock and he must be getting back to Richmond the shadows are very short and it really is about 1pm. Next moment when Moore's wife complains to her husband "You crossed him!" the shadows are long and it must be evening.
During the trial of More, after the guards at the back of the room turn around to face the roused crowd (1:57:22), they are facing forward again when the Chief Justice speaks, and facing the rear immediately after, with no time in which to turn.
In the beginning of the film, when the messenger is being rowed to Thomas More's house, the sun is setting in the sky, it is obvious that daylight is fading. When the messenger arrives at More's house, the daylight is no longer fading and instead the brightness of the day indicates early afternoon or even morning.
Lord Chancellor Wolsey did not die in office; he was removed from the office of Lord Chancellor by Henry (because of his displeasure at Wolsey's failure to secure a divorce from Catherine), and died more than a year after Sir Thomas More became Lord Chancellor. Wolsey did, however, remain Archbishop of York.
When Henry leaves More's estate, he twice indicates that it is eight o'clock. The shadows of most characters between his announcement and actual leaving are very short making it appear to be much closer to noon.