Character mistake: Patterson - the oceanographer - at one point claims that Lithuania is land-locked. She should know better; in fact, Lithuania has a coastline of close to 100 km on the Baltic Sea.
Factual error: Haloclines are referred to throughout, and depicted occasionally as some sort of underwater tornadoes. Haloclines are in fact just salinity gradients, and look nothing like they do on the show.
Character mistake: The characters state that the Atlantic is the deepest ocean, but it's in the Pacific Ocean that the deepest point, Challenger Deep, is located.
Continuity mistake: When Howard sees his ex in the jacuzzi, his glass has a little bit of alcohol in it. When he drops it and it shatters, the glass is empty.