Karai states that her father is in "kitchen utensils". The Shredder has been strongly associated with kitchen utensils. In Teenage Mutant Ninja Turtles (1987), in the Shredder's first encounter with the Turtles, seen in the episode Enter: The Shredder (1987), Raphael called him "a kitchen utensil".
When the Turtle Sub goes into stealth mode, the lighting makes the turtles look like they all have red bandanas, which was their look in the original Mirage "TMNT" comics.
When April steals the Pizza delivery boy's bike, she says "I'll bring it back someday!" This is a reference to the Pokémon (1997)'s first episode, where Ash stole Misty's bike and said these same lines.
The joke with the sea monster and the submarine was based on the Red Dwarf (1988) episode "Back to Reality", where the crew brings up the possibility that the monster may kill, eat, or mate with the ship.