Contradiction with Genesis 1:31
Genesis 1:31 describes everything as "very good," but Genesis 2:13 implies incompleteness or a need for further action by describing the river system specifically.
Genesis 1:31: And God saw every thing that he had made, and, behold, [it was] very good. And the evening and the morning were the sixth day. [And the evening...: Heb. And the evening was, and the morning was etc.]
Contradiction with James 3:11
James 3:11 questions the ability of the same source to produce both fresh and bitter water, while Genesis 2:13 describes multiple rivers coming from a single river.
James 3:11: Doth a fountain send forth at the same place sweet [water] and bitter? [place: or, hole]