Contradiction with John 7:27
Mark 13:21 warns against believing anyone who claims to know where Christ is, while John 7:27 suggests people thought they knew where the Messiah would come from.
John 7:27: Howbeit we know this man whence he is: but when Christ cometh, no man knoweth whence he is.
Contradiction with Luke 17:23-24
Mark 13:21 cautions against following claims of Christ being "here" or "there," but Luke 17:23-24 suggests that Christ's coming will be public and unmistakable, rendering such claims pointless.
Luke 17:23-24: And they shall say to you, See here; or, see there: go not after [them], nor follow [them].