Contradiction with Matthew 28:19
Mark 8:30 advises secrecy about Jesus' identity, while Matthew 28:19 commands the disciples to go and make disciples of all nations, baptizing them in Jesus' name.
Matthew 28:19: Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: [teach...: or, make disciples, or, Christians of all nations]
Contradiction with John 1:41
Mark 8:30 implies Jesus told them not to share His identity, yet Andrew went and told his brother Simon that they had found the Messiah.
John 1:41: He first findeth his own brother Simon, and saith unto him, We have found the Messias, which is, being interpreted, the Christ. [the Christ: or, the Anointed]
Contradiction with John 4:25-26
Mark 8:30 suggests keeping Jesus' identity concealed, while Jesus openly reveals His identity as the Messiah to the Samaritan woman.
John 4:25-26: The woman saith unto him, I know that Messias cometh, which is called Christ: when he is come, he will tell us all things.
Contradiction with Acts 1:8
Mark 8:30 calls for silence, whereas Acts 1:8 instructs the disciples to be witnesses of Jesus to the ends of the earth.
Acts 1:8: But ye shall receive power, after that the Holy Ghost is come upon you: and ye shall be witnesses unto me both in Jerusalem, and in all Judaea, and in Samaria, and unto the uttermost part of the earth. [power...: or, the power of the Holy Ghost coming upon you]
Contradiction with Luke 9:60
Mark 8:30 favors secrecy, but Luke 9:60 features Jesus telling a disciple to proclaim the kingdom of God.
Luke 9:60: Jesus said unto him, Let the dead bury their dead: but go thou and preach the kingdom of God.