Contradiction with John 13:36
This verse shows Peter explicitly asking Jesus where He is going, which contrasts with John 16:5 where Jesus says that none of the disciples asks Him where He is going.
John 13:36: Simon Peter said unto him, Lord, whither goest thou? Jesus answered him, Whither I go, thou canst not follow me now; but thou shalt follow me afterwards.
Contradiction with John 14:5
Thomas questions Jesus about not knowing where He is going, contradicting the statement in John 16:5 that none asks about His destination.
John 14:5: Thomas saith unto him, Lord, we know not whither thou goest; and how can we know the way?
Contradiction with John 14:28
Jesus discusses His departure with the disciples, indicating they are aware of His leaving, which contradicts the implication in John 16:5 that they are not questioning His departure.
John 14:28: Ye have heard how I said unto you, I go away, and come [again] unto you. If ye loved me, ye would rejoice, because I said, I go unto the Father: for my Father is greater than I.