Kenelm Digby, who proposes to use wounded dogs and the "powder of sympathy" to send time signals to ships, is shown as a middle-aged man in 1730, but he died in 1665.
The eighteenth century chronometer H4 is described as having a mechanical balance that ticks 5 times per second, however the second hand of the watch shown moves only once a second which is characteristic of a modern quartz movement.
In the final voice over, Dava Sobel talks about charting our three dimensional world. However, one of the major points of this movie is that, as far as navigation is concerned, only two dimensions, latitude and longitude, are required to chart it.
In a conversation occurring in approximately 1730, John Harrison refers to the number pi, the ratio of the circumference of a circle to its diameter. However, the notation pi was not in current use until it was adopted by Leonhard Euler in 1737.
The word "scientist" was not invented until 1840. In the 18th century they were still called "natural philosophers".
Harrison describes his clock to George Graham, and the accuracy astounds him. In reality, Harrison invented the "gridiron pendulum" (which made such accuracy possible) in 1726. However, Graham had invented the even more accurate "mercury pendulum" in 1721, so he would not have stated such accuracy "can't be done", when first meeting Harrison in 1730.
At the outset of William's voyage home with Capt. Bourke, the command, "Raise upper topsails!" can be clearly heard. Split topsails did not come into use until 100 years later.
Rupert Gould is shown contributing to the "Brains Trust" on
television. The "Brains Trust" was a radio series at the time of Gould's death in 1948, and did not become a television series until 1955.
During the entire movie, when H1 is seen, the ticking that can be heard belongs to H3. The actual H1 and H2 tick in a rather dull way, but H3 is instantly recognizable, which is probably why its sound was used for H1 and H2 too. H4 appears to use the correct sound.
When on his sea voyage, John Harrison gives an elegant and clear explanation of longitude to the crew of the ship, and later he makes short and clear remarks to the Board of Longitude. In reality, Harrison was very well known for his inability to express himself clearly and this was one of the reasons for his problems with the Longitude Committee.