During the brief horseback fight with Richmond, the colour of Richard's armour repeatedly alternates between black and silver.
Just before the Battle of Bosworth Richard observes that the sun is not shining and says that it will be a dark day. However, once the army is assembled on the field there is bright sunshine and all of the battle scenes are sunlit.
When Richard tells Lady Anne to kill him, she grabs the sword and it bends. It is even more noticeable when Richard puts the sword to his own neck.
For one shot at the end during the battle scene, right around the famous "My kingdom for a horse!" line, Richard's left hand has all five fingers. During the rest of the movie, Richard only has three fingers on his left hand as part of the character's deformities.
Richard claims he will "Set the murderous Machiavel to school" in a scene during the reign of Edward IV: Niccolò Machiavelli was only fourteen by the time of Edward's death. This error is copied from the William Shakespeare play.
For around half a second, shortly after Lady Anne follows the coffin from the courtyard into the hall there is a clearly visible rubber tyre tread pattern on the floor. The goof is at the bottom of the frame and slightly left of centre; presumably left by a rubber wheel on the camera dolly.
In the scene when Richard tells King Edward of Clarence's supposed treason, two monks are singing hymns from a large book: their lips are not only out of sync with their singing, but with each other.
When Richard and Buckingham are standing over Edward IV's deathbed, and Buckingham says 'To part the Queen's proud kindred from the princes', Ralph Richardson's lips are out of sync.