The original Jules Verne story "A Journey to the Centre of the Earth" (1864), on which the preceding movie Journey to the Center of the Earth (2008) is loosely based, never had a sequel. However, another Jules Verne story "20,000 Leagues Under the Sea" (1870), did have a sequel, called "The Mysterious Island", which was released in 1874 and followed five American men stranded on an island in the South Pacific, which is similar to a plot point in this movie.
There is another Jules Verne novel entitled "The Golden Volcano", which - although is set in the Canadian Arctic during the gold rush - spews gold nuggets when it erupts. This is likely where the mountains of gold came from for this movie.
When Sean announces that he is going the Mysterious Island, Hank jokingly says, 'maybe you stop by the moon and grab me a slurpee'. This foreshadows the next movie in the series Journey to the Center of the Earth: From the Earth to the Moon.
Dwayne Johnson and Branscombe Richmond both starred in the Scorpion King (2002) which is a spin-off film from the Mummy Returns (2001) in which Dwayne Johnson stars with Brenden Fraiser. Fraiser starred in the Journey to the Center of the Earth (2008) which Mysterious Island (2012) is a sequel to.
When they find the giant lizard eggs Hank (Dwayne Johnson) quips "It had to be a lizard. Why couldn't it have been snakes?" This is a take on the famous Indiana Jones line from Raiders of the Lost Ark (1981) in which Indy falls into a pit of snakes and says "Snakes. Why'd it have to be snakes?"