Parents probably don't have anything to be anxious over. The most violent thing a kid will do in this game is to pop a bubble while a sea critter is inside, but the rest of the time the game treats enemies as things to be avoided rather than killed. There are chase sequences involving a shark and an anglerfish that some may find a little intense. However, I honestly don't think it poses any real problems since both scenes were lifted from the movie itself.
If the movie was watched beforehand (with captions) though, the cut-scenes may not be a huge issue. The game doesn't appear to use audio cues either. The game also faithfully follows the movie script. It may be a good idea to watch the movie first before playing the game to avoid any spoilers.
Deaf and hard of hearing gamers will find plenty of subtitles during the game, and more importantly, when a level is first introduced. Level objectives are laid out pretty clearly through text, along with any scenes generated in-game. Unfortunately, I didn't notice any subtitles or captions available during the cut-scenes, nor did I notice a caption option in the menu.