Plot hole: The impetus of the plot is that the doctor mismatches the two sets of twins. But watch carefully the placement as they are born: first the DiCici baby, then the Coupe on the left, then the other DiCici, then the other Coupe on the right of the other three, making it, from the viewer's perspective, DiCici-Coupe-DiCici-Coupe. The doctor then switches the two middle ones, which supposedly mix the twins, but in fact it makes them DiCici-DiCici-Coupe-Coupe, and the two left and two right are given to the fathers. So the twins are not mismatched.
Plot hole: Brent discovers that Taylor is on the planet and has a connection to Nova through the dog tags she is wearing. However, throughout the first movie, Taylor never had any dog tags on his person. Also, his ship was destroyed, and he only managed to retrieve a life raft and supplies. His belongings and clothing were taken from him when he was apprehended by the apes. Taylor should never have had any dog tags to give to Nova or for Brent to discover. (00:11:10)