A red herring is a clue or piece of information that is intended to be misleading. In Chapter 16, we find Lombard and Vera are the only two characters left on the island, or so we think.
"Why did I never see his face properly before? A wolf - that's what it is - a wolf's face..... Those horrible teeth." (pg 262)
This makes the reader believe that Lombard is the murderer.
"This is the end, you understand. We've come to the truth now. And it's the end. " (pg 262)
This makes the reader believe that the murderer is one of the two characters left. We do not find out until later that this wasn't the end, yet.
Vera convinces Lombard to drag Dr. Armstrong's body out of the water. Then,
"Her tone warned him. He spun around. Even as he clapped his hand to his pocket he knew that he would find it empty. She had moved a yard or two away and was facing him, revolver in hand." (pg 264)
The red herring here is that the reader thinks that Vera is the murderer. She does end up killing Lombard.
"Relief possessed Vera -- enormous exquisite relief. At last it was over." (pg 265)
The red herring is that the reader thinks it is over, and everyone is dead except Vera. She is safe and filled with relief. The reader starts to let down.
Vera then starts to recite the poem. She remembers it incorrectly.
"One little soldier boy left all alone. How did it end? Oh yes! He got married and then there were none." (pg 267)
This misleads the reader into thinking there will be a happy ending. She then gets very tired and thinks that Hugo is in the house waiting for her. When she puts the noose around her neck, it says,
"Hugo was there to see she did what she had to do." (pg 269)
This misleads the reader because Hugo is nowhere around. Vera kicks the chair out from under herself. Justice Wargrave was in the closet and put the chair back in its place, but Hugo had nothing to do with it.
The page numbers are for my edition of the book. Chapter 16 is not that long, and you should be able to find most of them easily.