Plot hole: In order for the treasure trail to be followed both desks would need to have existed in 1865 when the code was deciphered. However HMS Resolute wasn't broken up and made into desks until 1879.
Suggested correction: In the movie, the code-written in the 1860s-leads to Laboulaye's lady, which was already conceptualised in 1865. The statue, which was theoretically inscribed after the Resolute wreck was made into desks, then points to them.
Continuity mistake: In the first film, John Adams Gates (Christopher Plummer) tells his grandson, young Ben, about how a boy named Thomas Gates learned about the Templar treasure from Charles Carroll in 1832. John refers to Thomas as "my grandfather's grandfather," making him Ben's Great-Great-Great-Great-Grandfather. The adult Thomas Gates is in the prologue of the sequel deciphering Booth's diary in 1865. His son, Charles, is said to be the grandfather of Patrick Gates, played by Jon Voight. That would make Thomas only Ben's great-great-grandfather, which another character refers to him as later in the second movie, which in turn makes Thomas Gates just the grandfather of John Gates. Either John Gates' memory is fuzzy in his old age or two generations of Gates men disappeared from the timeline. Perhaps John meant to say it was Ben's grandfather's grandfather, which is how Thomas is related to Ben in this movie.