William Lamd, Lord Melbourne was Prime minister until 1841. In the movie he left this position before Queen Victoria's marriage.
At her coronation in 1838 Queen Victoria was wearing a golden ornamented dress, not a black one as shown in the movie.
Lord Melbourne mentioned that Prince Albert is 25 before they met. However in real life in 1837 he was 28 and when he married he was 32.
In the movie Queen Victoria remains in the Kensington Palace, while in real life she moved to Buckingham Palace soon after she became queen.
Queen Victoria and Prince Albert first met in 1840 and got married one year later, not in 1837 as suggested in the movie.
Victoria mentioned how excited she was at her confirmation. This event happened in 1856, almost 20 years after the movie's setting.
Around 1h 3min when Victoria and Albert rekindle the fire alternating paper and wood part of a moving crew member as well as a blinking light on equipment attached to a cable are visible in the mirror behind them.