Other mistake: There's a scene where they turn a wheel to control the flow of water into a much larger chamber. The cavern that is presumably completely filled with water (water is dripping off the ceiling) is massive. The flow from the smaller chamber into the cavern is relatively small. They enter moments after stopping the flow to find the cavern is drained. It should A) either take the cavern a very long time to drain or B) the cavern should never have been fully filled with water.
Other mistake: During the car chase in London, when Ben almost hits the dogs, we see one dog running up to the car and licking the backup-camera. However since the camera is actually mounted above the license plate, it's impossible to reach for a dog this size.
Answer: Gates' name was added by Wilkinson to get Ben to do all the work in finding the treasure (as that would prove Thomas's innocence).
Sereenie
I disagree, Gate's name was always on the page. Presumably the investigation of the page would have revealed that it was a recent addition not a contemporary part of the text if this were not the case. Perhaps a simpler explanation is just that the conspirators needed to consult gates due to his deciphering skills, hence his name on the page, which explains the name "mastermind" as well.
Thomas Gates was on the page listed as "Artifex" which just means a practitioner of a craft. Mitch tries to say it's a "mastermind" but that's not 100% true, it could be but also just an expert at something. The museum curator who says, "we'll have this authenticated" was paid off by Mitch, so Mitch could very well have added the name and the curator lied.
Mitch says in the movie that adding Thomas's name to the page was the only thing he could think of to get Ben "in on the hunt." He says it at the end of the movie when he is apologizing for smearing Ben's "great great granddaddy's" good name.
Why does finding the treasure prove Thomas Gates' innocence anyway?